1/4 + 1/16 + 1/256 + ...

$1/undefined$ + $1/undefined$ + $1/undefined$ + $1/undefined$ + ... is an equation which is related to 1/2 + 1/4 + 1/8 + ... but adds up to $1/undefined$ and the denominators are the powers of 4.

Proof that sum is 1/3
Take the sum to be s. s = 1/4 + 1/16 + 1/256 + ... But, you can multiply by 4 to get this: 4s = 1 + 1/4 + 1/16 + 1/256 + ... This results in the equation 4s = s + 1, so 3s = 1.

The answer will be s = 1/3.