   Chapter 13.3, Problem 4E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# CONCEPTS(a) The n t h partial sum of a geometric sequence a n = a r n − 1 is given by S n =         _ .(b) The series ∑ k = 1 ∞ a r k − 1 = a + a r + a r 2 + ... is an infinite           _ series. If | r | < 1 , then this series           _ , and its sum is S =         _ . If | r | ≥ 1 , the series         _ .

To determine

(a)

To fill:

The blanks in the given sentence.

Explanation

Given:

The sentence is,

The nth partial sum of a geometric sequence an=arn1 is given by Sn=_.

Approach:

A geometric sequence is a sequence of the form

a, ar, ar2,…

The number a is the first term, and r is the common ratio of the sequence.

The nth term of the a geometric sequence is given as,

an=arn1.

And sum of the geometric sequence is Sn=a(1rn)(1r)

To determine

(b)

To fill:

The blanks in the given sentence.

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