Alternating Series Test Determine whether the

Chapter 10, Problem 19E

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QUESTION:

11-24. Alternating Series Test Determine whether the following series converge.

\(\sum_{k=1}^{\infty}(-1)^{k+1} \frac{k^{10}+2 k^{5}+1}{k\left(k^{10}+1\right)}\)

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QUESTION:

11-24. Alternating Series Test Determine whether the following series converge.

\(\sum_{k=1}^{\infty}(-1)^{k+1} \frac{k^{10}+2 k^{5}+1}{k\left(k^{10}+1\right)}\)

ANSWER:

Problem 19E

Alternating Series Test Determine whether the following series converge.

Answer;

     Step 1;

              In this  problem we have to find whether the series  converge or not.

Alternating series test:

Suppose that for there exists a N so that for all

  1. is positive and  monotone  decreasing
  2. .

     Then the alternating  series    converges.

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