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Chapter 12: Q. 175 (page 1199)

Find the sum of each infinite geometric series.

1,024+512+256+128+64+32+.....

Short Answer

Expert verified

The sum of the infinite series is2048.

Step by step solution

01

Step 1. Given information

The infinite geometrical series is 1,024+512+256+128+64+32+.....

The sum Sof the infinite geometrical series having first terma1and the common ratio ris localid="1646580728248" S=a11-r,r<1.

02

. To find a1 and r. 

The first term is a1=1024and the common ratio is

r=5121024r=12

Because 12鈮�1, so the infinite geometric series have sum.

03

Step 3. To find the sum.

We have,

S=a11-rS=10241-12S=102412S=2048

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