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Explain how you could adapt the root test to analyze a seriesk=1akin which the terms of the series are all negative.

Short Answer

Expert verified

Hence proved.

Step by step solution

01

Step 1. Given information.

We are givenk=1ak.

02

Step 2. Explanation.

According to the root test,

1. IfL<1series converges.2. IfL>1series diverges.3. IfL=1the test is inconclusive.

Where, Series is k=1akand L=limkak1k.

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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