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Chapter 12: Q. 176 (page 1199)

Find the sum of each infinite geometric series:

6,561+2187+729+243+81+27+...

Short Answer

Expert verified

The sum of infinite geometrical series is9841.50.

Step by step solution

01

Step 1. Given information.

The infinite series is6,561+2187+729+243+81+27+...

The sum Sof the infinite geometrical series having first terma1 and the common ratiorisrole="math" localid="1646581845578" S=a11-r,r<1.

02

Step 2. To find a1 and r.

The first term is a1=6561 and the common ratio is

r=21876561r=13

Because13鈮�1, so the infinite geometric series have sum.

03

Step 3. To find the sum.

We have,

S=a11-rS=65611-13S=656123S=9841.50

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