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Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satisfied 1 + e 6k k=1Determine...

Question

Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satisfied 1 + e 6k k=1Determine which of the necessary properties of the function that will be used for the Integral Test has. Select all that apply:The function f(x) is positive for x2 1 The function f(x) is continuous for x21_ The function f(x) has the property that ak = f(k) for k = 1,2, 3, The function f(x) is a decreasing function for x2 1. The function f(x) i

Use the Integral Test to determine whether the following series converges after showing that the conditions of the Integral Test are satisfied 1 + e 6k k=1 Determine which of the necessary properties of the function that will be used for the Integral Test has. Select all that apply: The function f(x) is positive for x2 1 The function f(x) is continuous for x21_ The function f(x) has the property that ak = f(k) for k = 1,2, 3, The function f(x) is a decreasing function for x2 1. The function f(x) is negative for xz 1 The function f(x) is an increasing function for x 2 1. Select the correct choice below and, if necessary; fill in the answer box to complete your choice. OA The series converges. The value of the integral 5 e dx is (Type an exact answer:) 0 B The series diverges The value of the integral dx iS 1 +



Answers

Integral Test Use the Integral Test to determine whether the following series converge after showing that the conditions of the Integral Test are satisfied. $$\sum_{k=1}^{\infty} \frac{1}{\sqrt[3]{5 k+3}}$$

The limit as be approaches infinity of the integral from one to be off Eat the power of native X squared the axe So this is equal to the square root of pi multiplied by some function off axe divided by two evaluated from one to be so, um

In our comparison sized we have, hey, we have the integra from once infinity of E. Exponents. My nest eggs, the eggs. And this is equal to the limits. Samu Finnessey we approaches infinity. And so you're going from one to be mm S. D. S. And this is equal to their limits as B approaches infinity of minutes. Mm hmm. Yes, From 1 to be. And this is going to give us the limits as B approaches infinity of my needs. E. S. P names, my name is B Class E S P N is minus someone. Okay, so if we take the limits as B approaches infinity this is equal to one. But because because we have Because he experienced -12, it's less than or greater than E exponent minus X On the interval for 1, 2 infinity once you feel it, see. And since the insignia, once the infinity of E experience minus X. The X convergence contagious them. This implies that this implies that the Integra wants the infinity of E. Exponent minus X. To the power to the S also convey gis. Then for our second part we have the Integra once infinity of one over X. to the par five dean eggs. Okay, so from from dates principle that if I have an integra once infinity of one over eggs the eighth. Well said it's diverges if P so diverges diverges for P not equal to one. Okay, so it's a similar example we had earlier in exercise 49. So that any time I have won the integral one over Once. The infinity of one over X. to the power p the eggs. N. A. P. one over p. My next one converges If we have 1 -2. To be less than zero or P. To be greater than one. So from this example you realize that for B paths the ace here there's five this five which is a pity Is greater than one. So it's converges. So this converges this convey gis which then implies that because this converges them. We are saying that because it's converges then it's in place that It's in places one over extra part five plus one is less than one over X. To the power five on the interview for want to infinity. This implies that Hawaiian Segre Once infinity of one over extra par five plus one. The s also convey gis Okay, so since this convergence we are seeing if you compare, then this also converges as well.

In a comparison sized we have, hey, we have the Integra from once infinity of E. Exponents. My nest eggs, the eggs. And this is equal to the limits. Samu Finnessey, we approaches infinity. And so you go from one to be mm S. D. S. And this is equal to their limits as B approaches infinity of minutes. Mm Yes, From 1 to be. And this is going to give us the limits as B approaches infinity of my needs E. S. P names, my name is B Class E S P s minus someone. Okay, So if we take the limits as B approaches infinity, this is equal to one. But because because we have Because he experienced -12, it's less than or greater than E exponent minus X. On the interview for 1 2 infinity once you feel it. See And since the insignia, once the infinity of E experience minus X. The X convergence contagious them. This implies that this implies that the Integra wants the infinity of E. Exponent minus X. To the power to the S also convey gis. Then for a second part we have the integra once infinity of one over X. to the par five dean eggs. Okay, so from from dates principle that if I have an Integra once infinity of one over eggs the eighth. Well said, it's diverges FP. So diverges diverges for P not equal to one. Okay, so it's a similar example we had earlier in exercise 49 so that any time I have won the integral one over once the infinity of one of our X. To the power P the eggs. N A P one over P my next one converges If we have 1 -2. To be less than zero, Or P to be greater than one. So from this example, you realize that for B paths the ace here there's five. This five which is a P Is greater than one. So it's converges. So this converges this convey gis, which then implies that because this converges them, we are saying that because it's converges then it's in place that It's in places one over extra, Part five plus one is less than one over X to the power five on the interval ever want to infinity. This implies that Hawaiian Segre Once infinity of one over Extra Power five Plus 1. The S also convey Gis, Okay, so since this convergence we are seeing if you compare, then this also converges as well.

In a comparison sized we have, hey, we have the Integra from once infinity of E. Exponents. My nest eggs, the eggs. And this is equal to the limits. Samu Finnessey, we approaches infinity. And so you go from one to be mm S. D. S. And this is equal to their limits as B approaches infinity of minutes. Mm Yes, From 1 to be. And this is going to give us the limits as B approaches infinity of my needs E. S. P names, my name is B Class E S P s minus someone. Okay, So if we take the limits as B approaches infinity, this is equal to one. But because because we have Because he experienced -12, it's less than or greater than E exponent minus X. On the interview for 1 2 infinity once you feel it. See And since the insignia, once the infinity of E experience minus X. The X convergence contagious them. This implies that this implies that the Integra wants the infinity of E. Exponent minus X. To the power to the S also convey gis. Then for a second part we have the integra once infinity of one over X. to the par five dean eggs. Okay, so from from dates principle that if I have an Integra once infinity of one over eggs the eighth. Well said, it's diverges FP. So diverges diverges for P not equal to one. Okay, so it's a similar example we had earlier in exercise 49 so that any time I have won the integral one over once the infinity of one of our X. To the power P the eggs. N A P one over P my next one converges If we have 1 -2. To be less than zero, Or P to be greater than one. So from this example, you realize that for B paths the ace here there's five. This five which is a P Is greater than one. So it's converges. So this converges this convey gis, which then implies that because this converges them, we are saying that because it's converges then it's in place that It's in places one over extra, Part five plus one is less than one over X to the power five on the interval ever want to infinity. This implies that Hawaiian Segre Once infinity of one over Extra Power five Plus 1. The S also convey Gis, Okay, so since this convergence we are seeing if you compare, then this also converges as well.


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