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Fill in the blanks: Let f be a function with domain [1,). If the function f is ______ and ______ , and if ______ converges, then the series _______ converges absolutely.

Short Answer

Expert verified

On completing the fill in the blanks, we get, "Let f be a function with domain [1,). If the function f is monotonically and decreasing , and if limxfx=0converges, then the seriesx=1fx converges absolutely. "

Step by step solution

01

Step 1. Given information.

Consider the given question,

Domain is[1,).

02

Step 2. Fill in the blanks.

If the function fis monotonically decreasing and limxfx=0and the integral x=1fxdxconverges, then the series x=1fxconverges absolutely by integral test.

Therefore, the first blank is completed by monotonically and decreasing, second blanks bylimxfx=0and third isx=1fx.

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