Question

find the sum of the series 1-2/2+1/4+1/8.... to n terms.

Answer 1

I suspect a typo in the 2nd term.
Did you mean ...

1+1/2+1/4+1/8.... I will suspect as much

then a = 1 , r = 1/2

sum of n terms
= 1(1 - (1/2)^n )/(1 - 1/2)
= 2(1 - (1/2)^n )
= 2 - (1/2)^(n-1) or 2 - 2^(1-n)

testing my answer:
sum of first 4 terms, n = 4
= 1 + 1/2 + 1/4 + 1/8 = 15/8

using my answer:
sum = 2 - 2^-3
= 2 - 1/8 = 15/8

Answer 2

sir this question answer (2/3(1-(-1)^n/2^n)