Choose your test Use the test of your choice

Chapter 12, Problem 40E

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QUESTION:

40-57. Choose your test Use the test of your choice to determine whether the following series converge.

\(\sum_{k=1}^{\infty} \frac{(k !)^{3}}{(3 k) !}\)

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QUESTION:

40-57. Choose your test Use the test of your choice to determine whether the following series converge.

\(\sum_{k=1}^{\infty} \frac{(k !)^{3}}{(3 k) !}\)

ANSWER:

Problem 40E

Choose your test Use the test of your choice to determine whether the following series converge.

Answer;

Step 1;

In this problem we have to determine whether the seriesconverge or not.

Let us use ratio test to find the whether the series converge or not.

Ratio test:

Let be a sequence of nonzero terms and let . Then

  1. If L < 1 then  is convergent.
  2. If L > 1 then  is divergent.
  3. If L = 1 then nothing can be said about the series. In other words, we say that the ratio is inconclusive.

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