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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

SKILLS

65-76 ■ Infinite Geometric Sequence Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum.

1 1 3 + 1 9 1 27 +

To determine

Whether the infinite geometric series is convergent or divergent and its sum, when it is convergent.

Explanation

Given:

The sum of the infinite geometric series is given as,

113+19127+

Approach:

If |r|<1, then the infinite geometric series converges.

k=1ark1=a+ar+ar2+ar3+

The sum of the infinite geometric series, when it is convergent is given as,

S=a1r ……(1)

Here, S is the sum of infinite geometric series, a is the first term of the sequence and r is the common ratio of the sequence.

If |r|1, then the infinite geometric series diverges.

Calculation:

Since the first term of the sequence is 1 and the common ratio is (13)

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