It's easier than what you think

Algebra Level 1

Solve -

$\sum _{ n=1 }^{ \infty }{ \frac { 1 }{ { 2 }^{ n } } }$

2 solutions

Aryan Gaikwad
Mar 8, 2015

Nice solution :) +1

A Former Brilliant Member - 6 years, 3 months ago

Hey in the question it's $1/2n$ rather than $1/2^n$ according to your solution. Please correct the question.

Kislay Raj - 6 years, 3 months ago

I'm extremely sorry. It's fixed now.

Aryan Gaikwad - 6 years, 3 months ago

Nelson Mandela
Mar 8, 2015

The series is an infinite GP where a(first term) = 1/(2)^1 = 0.5.

r(common ratio) = 1/2.

So, sum = a/(1-r) = 0.5/0.5 = 1.