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Chapter 7: Q. 7 (page 639)

Explain how you could adapt the ratio test to analyze a series∑k=1∞akk in which the terms of the series are all negative.

Short Answer

Expert verified

Hence explained.

Step by step solution

01

Step 1. Given information.

The given series is ∑k=1∞ak.

02

Step 2. Explanation.

The ratio test is given by:

1. IfL<1series converges.2. IfL>1series diverges.3. IfL=1the test is inconclusive.whereL=limk→∞ak+1akand∑k=1∞akistheseries.

Now,

But if the series has all the terms negative, then negative sign can be adjusted and Root test can be used on the series∑k=1∞-ak.

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