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Chapter 7: Q. 63 (page 604)

Prove that the geometric sequence rkk=0鈭�diverges when r < 鈭�1.

Short Answer

Expert verified

Geometric sequence rkk=0鈭�diverges when r<-1

Step by step solution

01

Step 1. Given information

rkk=0鈭�

02

Step 2. proof

The given sequence is a geometric sequence and is converging to Lfor r< -1. Therefore, it contradicts the fact that if r>1 then rkdiverges as the terms of sequence rkk=0鈭�are positive and increasing but converging L.

Therefore, the assumption is wrong.

Hence, proved.

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