+8 sum to n terms of the series 1/2+3/4+7/8+15/16.... is? solve it for me please
[answer: (2^-n)+n-1]
+33653 Write the series as:
(1-1/2) + (1-1/4) + (1-1/8) + ... + (1-1/2^n) → n - (1/2 + 1/4 + 1/8 + ... + 1/2^n)
The term in brackets is a geometric series whose sum is given by (1/2)*(1-1/2^n)/(1-1/2) → 1-1/2^n
So. (1-1/2) + (1-1/4) + (1-1/8) + ... + (1-1/2^n) → n - (1 - 1/2^n) or 2^(-n) + n - 1
.
+33653 Write the series as:
(1-1/2) + (1-1/4) + (1-1/8) + ... + (1-1/2^n) → n - (1/2 + 1/4 + 1/8 + ... + 1/2^n)
The term in brackets is a geometric series whose sum is given by (1/2)*(1-1/2^n)/(1-1/2) → 1-1/2^n
So. (1-1/2) + (1-1/4) + (1-1/8) + ... + (1-1/2^n) → n - (1 - 1/2^n) or 2^(-n) + n - 1
.
