Question

The sum of an infinite GP is 1- 1/3 + 1/9- 1/27+....is
But there are different answers in book

Answer 1

Answer:

3/4

Step-by-step explanation:

In general:

$\displaystyle 1 + x + x^2+x^3+\cdots = \frac{1}{1-x},\quad\mbox{for}\ -1<x<1.$

The series you have corresponds to putting x = -1/3.  So the sum is

$\displaystyle\frac{1}{1-(-\frac13)} = \frac{1}{1+\frac13}=\frac{1}{\frac43} = \tfrac34$