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Chapter 7: Q. 3 (page 631)

Explain how you could adapt the comparison test to analyze a series鈭�k=1鈭�ak in which all of the terms are negative.

Short Answer

Expert verified

We can apply comparison test on the series鈭�k=1nak

Step by step solution

01

Step 1. Given information

An general term of an series is given as鈭�k=1鈭�ak

02

Step 2. Verification

In comparison test 鈭�k=1鈭�akand 鈭�k=1鈭�bkbe two series with positive terms with the condition as 0鈮�ak鈮�bk for every value of k.If the series鈭�k=1nbkconverges then the series 鈭�k=1nakconverges.

In the series 鈭�k=1nak, all terms are negative. Thus, for all values of k, akis negative. Therefore, -ak is positive for all values of k.

Thus we can apply comparison test on the series鈭�k=1nak

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