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Fill in the blanks: Let k=1akand k=1bkbe two series such that 0__________ for every ______. If the series _____ converges absolutely, then the series converges absolutely.

Short Answer

Expert verified

On completing the fill in the blanks, we get, "Let k=1akand k=1bkbe two series such that 0akbkfor every k>0. If the series k=1bk converges absolutely, then the seriesk=1ak converges absolutely.

Step by step solution

01

Step 1. Given ifnromation.

Consider the given question,

k=1ak,k=1bk are the two series.

02

Step 2. Fill up the blanks.

Let k=1ak,k=1bkbe the two series such that 0akbkfor every k>0.

If the series k=1bkconverges absolutely, then the series k=1akconverges absolutely.

Therefore, the first blank is completed by ak, second blank by bk, third blank by k>0, fourth blank by k=1bkand fifth byk=1ak.

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