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Chapter 12: Q 170. (page 1199)

In the following exercises, find the sum of each infinite geometric series.

1+12+14+18+116+132+164+鈰�

Short Answer

Expert verified

The obtained sum is 2.

Step by step solution

01

Step 1. Given Information. 

Consider the given series.

1+12+14+18+116+132+164+鈰�

02

Step 2. Find the common ratio.

To find the common ratio, divide the second term by first.

r=121=12

And the ratio isr<1.

03

Step 3. Find the sum of infinite series.

The sum formula of geometric infinite series isS=a1-r.

Substitute the first term and the common ratio in the above formula.

S=11-12=12-12=2

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