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

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Answer 1 · 2017-09-08T07:05:55

See below

#(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#