There is no value of c such that the infinite series converges.
How to analyze the converge of an infinite series
Convergence is a characteristic of infinite series, in which a sum tends to be a given number when n tends to +∞.
In this question we must prove for which values of c the infinite series may converge.
There are different criteria to prove whether a given series converges or not, one of the most used criteria is the ratio criterion, which states that:
[tex]r = \frac{a_{k+1}}{a_{k}}[/tex], where the series converges if and only if r > 1. (1)
If we know that [tex]a_{k} = k\cdot \ln c[/tex], then the rational formula is:
[tex]r = \frac{(k+1)\cdot \ln c}{k\cdot \ln c}[/tex]
[tex]r = 1 + \frac{1}{k}[/tex]
We notice that resulting expression does not depend on c and is greater than 1. Therefore, there is no value of c such that the infinite series converges. [tex]\blacksquare[/tex]
RemarkIf [tex]c[/tex] is a positive real number and [tex]a_{k} = k\cdot \ln c[/tex], for what values of [tex]c[/tex], if any, does the infinite series [tex]\sum_{k=1}^{\infty} a_{k}[/tex] converge?
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There is no values of c, for the infinite series ∑k=1[infinity]ak to be converge when c is a positive real number.
What do you mean by infinite series?The infinite series is the sum of addition of a sequence in which the number of terms present are infinite.
[tex]a_1+a_2+a_3....+a_n[/tex]
Here, ([tex]a_n[/tex]) is the nth term of the sequence. For infinite series, the ratio criterion can be given as,
[tex]r=\dfrac{a_{k+1}}{a_k}[/tex]
If c is a positive real number and
[tex]a_k=k\ln c[/tex]
Put the value in above shown ratio,
[tex]r=\dfrac{(k+1)\ln c}{k\ln c}\\r=\dfrac{k\ln c}{k\ln c}+\dfrac{\ln c}{k\ln c}\\r=1+\dfrac{1}{k}[/tex]
With the value of r, we can say whether the series is converge or not. This value of r does not depends on c.
Thus, there is no values of c, for the infinite series ∑k=1[infinity]ak to be converge when c is a positive real number.
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a measuring cylinder has a mass of 180g when empty. When a liquid is poured into the cylinder, the level rises to the 95m³ mark. Total mass is now 292g. What is the density of the of the liquid in g/cm³
Answer:
d (density) = m / V = (292 - 180) g / 95 cm^3 = 1.18 g / cm^3
(water is 1 gm / cm^3)
what direction can Earth's plates move
The movement of the plates creates three types of tectonic boundaries: convergent, where plates move into one another; divergent, where plates move apart; and transform, where plates move sideways in relation to each other. They move at a rate of one to two inches (three to five centimeters) per year.
Give two examples that provide evidence for the presence of terrestrial magnetism?
Explanation:
When a magnetic body is buried inside the earth in North-South direction, it gets magnetized due to the effect of terrestrial magnetism. A freely suspended magnet faces North-South direction.
Circuit A has a voltage of 10 V, and circuit B has a voltage of 15 V Which statement about the circuits is correct? (1 point)
If the resistance in circuit A equals the resistance in circuit B, then the current in circuit A is greater than the
current in circuit B.
If the resistance in circuit A is greater than the resistance in circuit B, then the current in circuit A is greater
than the current in circuit B.
If the current in circuit A equals the current in circuit B, then the resistance in circuit A equals the resistance
in circuit B
If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than
the resistance in circuit B.
If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than the resistance in circuit B.
Ohms LawOhms law states that the volatge in a circuit is directly proportional to the current flowing in the circuit.
V = IR
Where;
V is voltageI is currentR is resistanceThe given voltage in the circuits
Circuit A = 10 VCircuit B = 15 VAt equal resistance, the current flowing in circuit B will be greater than circuit A since circuit B has more voltage.
However, If the current in circuit A is greater than the current in circuit B, then the resistance in circuit A is less than the resistance in circuit B.
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Rock layer that must be rich in organic matter that was subjected to heat and pressure over time during the formation of oil and natural gas.
The lowest rock layer is a layer that must be rich in organic matter that was subjected to heat and pressure over time during the formation of oil and gas.
What is the lowest rock layer?The lowest rock layer refers to the lowermost part of the Earth's mantle, which is a thin rock layer (approximately 250 km).
In the Earth, the layers of rocks are progressively deposited, thereby pressing them to the bottom to generate sedimentary rocks.
The lowest rock layers on the bottom must be rich in organic matter to form fossil fuels.
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2 eggs cook in a frying pan, which is sitting over a gas burner. Is thermal energy being transferred from the metal pan to the eggs by radiation in this image? Why or why not?
Answer:
No, the eggs are in direct contact with the metal pan, which is in direct contact with the gas flame, so this is conduction, not radiation
Reasons:
-Thermal energy is being transferred by conduction.
-Radiation transfers thermal energy by electromagnetic waves.
-Radiation does not transfer thermal energy by direct contact.
Radiation heat transfer is a process where heatwaves are emitted that may be absorbed, reflected, or transmitted through a colder "body". Sun heats the earth by electromagnetic waves. The sun does not come in physical contact with the Earth to transfer heat. (In my opinion, the Earth touching the sun would not be on my to-do list.)
Explanation:
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A hockey puck of mass 150 g is sliding south along the ice and slows at a rate of 1.2m/s2. What is the net force acting on the puck?
Answer: another force on puck?
Force is a vector quantity characterized by the rate of change of momentum.
Mathematically, it is the product of mass and acceleration.
F = m × a
=> F = (150/1000) × (-1.2)
=> F = -0.18 kg m/s²
=> F = -0.18 N
Determine the slope of end a of the cantilevered beam. E = 200 gpa and i = 65. 0(106) mm4
For E = 200 gpa and i = 65. 0(106) mm4, the slope of end a of the cantilevered beam is mathematically given as
A=0.0048rads
What is the slope of end a of the cantilevered beam?Generally, the equation for the is mathematically given as
[tex]A=\frac{PL^2}{2EI}+\frac{ML}{EI}[/tex]
Therefore
A=\frac{10+10^2+3^2}{2*240*10^9*65*10^6}+\frac{10+10^3*3}{240*10^9*65*10^{-6}}
A=0.00288+0.00192=0.0048rads
A=0.0048rads
In conclusion, the slope is
A=0.0048rads
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The value of slope of end a of the cantilevered beam when E = 200 gpa and i = 65. 0(106) mm4 is 0.0048 rads.
How to find the slope at the end of the cantilevered beam?The formula used to find the slope at the end of the cantilevered beam is,
[tex]A=\dfrac{PL^2}{2EI}+\dfrac{ML}{EI}[/tex]
Here, (M) is the momentum, (EI) is flexural rigidity, (P) is concentrated load and (L) is the length of the beam.
Concentrated load is 10 KN and uniform load is 3 kN/m. E = 200 gpa and i = 65. 0(106) mm4.
[tex]A=\dfrac{10+10^2+3^2}{2\times240\times10^9\times65\times10^6}+\dfrac{10+10^3\times3}{240\times10^9\times65\times10^{-6}}\\A=0.00288+0.00192A=0.0048 \rm\; rads[/tex]
Thus, the value of slope of end a of the cantilevered beam when E = 200 gpa and i = 65. 0(106) mm4 is 0.0048 rads.
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How long does it take for jupiter to rotate on its axis.
Answer:
10 hours.
Every 10 hours, Jupiter will rotate at least once. It takes 12 years for Jupiter to make a revolution. This is because Jupiter is a gas, non-solid planet and also has a very large mass.
Answer: 10 Hours
Explanation:
Jupiter is the fastest spinning planet in the solar system
When do humans store fat molecules in their bodies? (1 pt. ) *
1. Humans store fat molecules every time they eat anything that contains Calories.
2. Humans store fat molecules when they eat food with a lot of fat.
3. Humans store fat molecules when they eat junk food.
4. Humans store fat molecules when they eat more Calories than they need.
How does a white dwarf compare to our sun as it exists now?.
Answer:
answer down below
Explanation:
it has similar mass but the white dwarf is much denser
Who developed the principle of whenever 2 objects come into contact with one another, materials are exchanged between them?.
Answer:
Edmond Locard
Explanation:
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Why do you only see one side of the moon? Lesson 3. 05 Question 12 options:
A:The moon only has one side
B:The rotational period is greater than to the period of revolution for the moon
C: The rotational period is equal to the period of revolution for the moon
D:The rotational period is less than the period of revolution for the moon
Answer:
The Moon orbits Earth once every 27.3 days and spins on its axis once every 27.3 days. This means that although the Moon is rotating, it always keeps one face toward us. Known as “synchronous rotation,” this is why we only ever see the Moon's nearside from Earth.
I hope this helps you out
What is stated in the 1st Law of Motion?
Answer:
Newton's first law: the law of inertia
Newton's first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.
Explanation:
Anything aka if a body is at constant speed in a straight line it would probably remain or keep moving in a straight line unless something slows it down like Fricton.
It is diffult to measure the volume of gas.Why?
Answer:
The volume of a gas is dependent on pressure and temperature.
Explanation:
Pressure and temperature affect different gases differently giving varied conclusions to the exact volume of that gas.
:-befrank
Calculate the mass (in g) of 346 cm³ of polythene. The density of polythene is 0.95 g/cm³. Give your answer to 2 decimal places.
Answer:
M = 328.70g
Explanation:
From the given values:
V = 346 cm³
M of 1 cm³ of Polythene = 0.95g or 95/100g
Solve:
M = (95×346)
10
= 32870
100
M = 328.70g
Amber is a
(a) metal
(b) rubber
(c) resin
(d) sugar
Answer:
c. Resin.
Explanation:
Amber is a resin.
Use the claim to answer the question.
Claim: Electromagnetic radiation can be described by a wave model or a particle model, depending on the situation.
Is this a scientific claim?
(1 point)
Yes, it can be backed up by experiments and evidence.
No, radiation is invisible, so there is no evidence to back up the claim.
Yes, any statement made by a scientist is a claim.
No, models can't be part of a scientific claim.
Scientific evidence such as reflection and photoelectric effect has proven the wave-particle model of electromagnetic radiation to be true.
What is electromagnet radiation?Electromagnetic radiation is radiation produced as a result of the interactions of the electric and magnetic fields.
Some forms of electromagnetic radiation include:
radio wavesmicrowavesultraviolet radiationvisible lightElectromagnetic radiation can be described using a wave model or a particle model.
The wave property of electromagnetic radiation include:
diffraction reflectionrefractionThe particle property of electromagnetic radiation include:
photoelectric effectCompton effect.Therefore, the wave-particle model of electromagnetic radiation is correct because it can be backed up by experiments and evidence.
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Answer:
I just took the identifying Claims Quick check
Explanation:
1. Claim: Electromagnetic radiation can be described by a wave model or a particle model, depending on the situation.
Is this a scientific claim?
Yes, it can be backed up by experiments and evidence.
2. A student states, "The wave model is better than the particle model for electromagnetic radiation because it is easier to understand." Is the student's statement a scientific claim?
No, it isn't because the statement is an opinion.
3. A student wants to make a scientific explanation regarding the wave model of electromagnetic radiation. Which of the following would be part of the scientific explanation?
Claims
4. A student makes this statement before conducting an experiment on electromagnetic radiation: "We expect the laser to diffract when passed through a slit." Which of the following explains why the student's statement is not a claim?
It is a prediction or hypothesis.
5. Which claim do scientists use to describe electromagnetic radiation?
Electromagnetic radiation exhibits properties of both particles and waves.
6. A physician is going to use high-frequency electromagnetic radiation to treat cancer in a patient. Which is a claim about this event?
A wave model is most useful for describing the frequency of the radiation.
How much force would you need to cause a 20-kilogram object to accelerate in a straight line to 20 m/s2?
Answer:
400N
Explanation:
Newton's second law of motion
F = ma
20 x 20 = F
F = 400
why is the freezing compartment kept at top in a refrigerator?
Answer:
Because Geography says the higher one goes the colder it gets
Answer:
The nature of convection.
Explanation:
Warm air rises; cold air falls, so the freezer at the top provides cold air for the other compartments at the bottom.
Extension Question
If the scale used to measure the mass of the unknown material maxes out at a
lower value than the actual mass of the material, then...
o the measured specific heat will be greater than the actual specific heat.
o the measured specific heat will be less than the actual specific heat.
The measured specific heat will be less than the actual specific heat if a lower value is gotten than the actual mass.
What is Specific heat capacity?This is defined as the quantity of heat needed to raise a substance's temperature by 1 degree Celsius.
If a substance has a low specific heat capacity , it loses water easily which makes the mass when measured to be smaller than the actual value.
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Hello people ~
what's the value of acceleration due to gravity on earth?
Answer:
9.8 m/s2
Its value is 9.8 m/s2 on Earth. That is to say, the acceleration of gravity on the surface of the earth at sea level is 9.8 m/s2. When discussing the acceleration of gravity, it was mentioned that the value of g is dependent upon location.
Should the kinetic coefficient of friction and the static coefficient change with a different mass
Explanation:
No. Surface contact area also no. The main issue is the types of materials in contact. Surface roughness somewhat matters. Certain surfaces such as ice are special in that pressure melts the ice.
Gwen runs back and forth along a straight track. During the time interval 0≤t≤45 seconds, gwen’s velocity, in feet per second, is modeled by the function v given by v(t)=250sin(t2120)t 6
Gwen's position is a function of his velocity and time
Gwen's position at 45 seconds is 63.9 feet
How to determine Gwen's position at 45 seconds?The function is given as:
v(t) = 250sin(t^2/120)/(t + 6)
When t = 45, we have:
v(45) = 250sin(45^2/120)/(45 + 6)
Evaluate the sum, the exponent and the quotient
v(45) = 250sin(16.875)/(51)
Evaluate the sine ratio
v(45) = 250 * 0.2903/51
Evaluate the product and quotient
v(45) = 1.42
The position is then calculated as:
S(45) = v(45) * 45
This gives
S(45) = 1.42 * 45
Evaluate the product
S(45) = 63.9
Hence, Gwen's position at 45 seconds is 63.9 feet
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The displacement is the shortest between any two given points. The displacement of Gwen at the time period of 45 seconds is 63.9 feet.
What is displacement?The displacement is the shortest between any two given points. It is the product of velocity and time.
Given that the function of the velocity is [tex]v(t)=\dfrac{250\sin\left(\frac{t^{2}}{120}\right)}{\left(t+6\right)}[/tex]. Therefore, substitute the value of t as 45, to know the velocity of Gwen at 45 seconds,
[tex]v(t)=\dfrac{250\sin\left(\frac{t^{2}}{120}\right)}{\left(t+6\right)}[/tex]
[tex]v(45)=\dfrac{250\sin\left(\frac{45^{2}}{120}\right)}{\left(45+6\right)}\\\\v(45) = 1.42[/tex]
Since displacement is the product of velocity and time, therefore, the displacement is equal to,
[tex]s = v \times t\\\\s = 1.42 \times 45\\\\s = 63.9\rm \ feet[/tex]
Hence, the displacement of Gwen at the time period of 45 seconds is 63.9 feet.
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You are part of a police unit that has found a powder in a suspect's home. You think it might be a new drug called XYZ. XYZ is an ionic compound that dissolves in water. However, what you think might be a drug may just be salt. Unfortunately there seems to be iron fillings and sand mixed in with the white powder. Your job is to isolate the white powder before sending it to the police lab to be tested to determine if it is salt or XYZ. Give step by step directions on exactly how you will separate your mixture of white powder, iron fillings, and sand.
The steps in the separation include;
Use of magnetaddition of water and filtrationEvaporationSeparation techniquesSeparation techniques has to do with how to obtain a substance in the presence of other substances. In this case, we have the substance XYZ mixed with iron filling and sand.
The separation process begins by using a magnet to remove all the iron fillings. Secondly, water is added and the substance XYZ dissolve in water since it is ionic. The sand can be separated form the solution by filtration.
Lastly, the solution is evaporated and the pure XYZ is obtained and sent to the police lab for analysis.
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what is electric charge?
Answer:
Electric Charge is the property associated with matter due to which it produces and experiences electric and magnetic effect
Who discovered the basic laws of planetary orbits?.
Answer:
Johannes Kepler
What led to Henry Ford’s success as an entrepreneur?
His personal wealth.
His innovative production methods.
His commitment to improving labor laws.
What happens when volcanoes release greenhouse gases into the atmosphere?
The climate gets warmer.
The climate gets cooler.
Winter becomes longer.
Summer becomes longer.
His desire to pay high wages.
What led to Henry Ford’s success as an entrepreneur?
His innovative production methodsWhat happens when volcanoes release greenhouse gases into the atmosphere?
The climate gets warmerWhat is the velocity of ab 8 kg lead shoot-out if it has 484 j
Answer:
attached image
Explanation:
project: weather forcasting
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B that is the correct answer