The odd value of n for which `704 + 1/2 (704) + 1/4 (704) + ... upto n terms = 1984 - 1/2 (1984) + 1/4 ( 1984) - .... upto n terms is :

Explanation

`s_n=(a(1-r^n))/(1-r)`

`s_n^1=(704(1-(1/2)^n))/(1/2)=1408(1-(1/2)^n)`

`s_n^2=1984(1-(-1/2)^n))/(1+1/2)`

`s_n^1=s_n^2`

`1408(1-(1/2)^n)=3968/3(1-(-1/2)^n)`

n is odd

`4224-4224t=3968+3968t`

`t=256/8192=2^8/2^13`

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