Find the sum of the series (1+1/3)(1+1/3^2)(1+1/3^4)(1+1/3^8)...... oo?

1 Answer
Sep 8, 2017

See below

Explanation:

(1 - 1/3)(1 + 1/3)(1+1/3^2)(1+1/3^4).....oo
Multiplying by (1- 1/3)

The series changes as follows
(1-1/3^2)(1+1/3^2)(1+1/3^4).....oo
(1-1/3^4)(1+1/3^4)(1+1/3^8)....oo

And this goes on till infinity

Going by the pattern, the series can be written as

(1-1/3^oo)

Since we multiplied it by (1-1/3)
We need to divide it

So,

(1-1/3^oo)/(1-1/3)
(1-0)/(2/3)

Therefore the series reduces to

3/2