1/2 + 1/4 + 1/8 + ...

$1/undefined$ + $1/undefined$ + $1/undefined$ + $1/undefined$ + ... is an equation which is related to 1/4 + 1/16 + 1/256 + ... but adds up to 1 and the denominators are the powers of 2.

Proof that sum is 1
Take the sum to be s. s = 1/2 + 1/4 + 1/8 + ... But, you can multiply by 2 to get this: 2s = 1 + 1/2 + 1/4 + 1/8 + ... This results in the equation 2s = s + 1, so s = 1.