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Chapter 7: Q 54. (page 615)

Determine whether the series 鈭�k=0鈭�-98kconverges or diverges. Give the sum of the convergent series.

Short Answer

Expert verified

The series 鈭�k=0鈭�-98kdiverges.

Step by step solution

01

Step 1. Given information.

Given a series 鈭�k=0鈭�-98k.

02

Step 2. Find if the series converges or not.

The series 鈭�k=0鈭�-98kis in the standard form 鈭�k=0鈭�crkfor a geometric series with c=1and r=-98.

The geometric series converges if and only if r<1.

Since localid="1648966760738" r=-98, it follows that the series localid="1648966763917" 鈭�k=0鈭�-98kdiverges.

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