<Dd> 1 2 + 1 4 + 1 8 + 1 16 + ⋯ = ∑ n = 1 ∞ (1 2) n = 1 2 1 − 1 2 = 1 . (\ displaystyle (\ frac (1) (2)) + (\ frac (1) (4)) + (\ frac (1) (8)) + (\ frac (1) (16)) + \ cdots = \ sum _ (n = 1) ^ (\ infty) \ left ((\ frac (1) (2)) \ right) ^ (n) = (\ frac (\ frac (1) (2)) (1 - (\ frac (1) (2)))) = 1 .) </Dd> <P> As with any infinite series, the infinite sum </P> <Dl> <Dd> 1 2 + 1 4 + 1 8 + 1 16 + ⋯ (\ displaystyle (\ frac (1) (2)) + (\ frac (1) (4)) + (\ frac (1) (8)) + (\ frac (1) (16)) + \ cdots) </Dd> </Dl> <Dd> 1 2 + 1 4 + 1 8 + 1 16 + ⋯ (\ displaystyle (\ frac (1) (2)) + (\ frac (1) (4)) + (\ frac (1) (8)) + (\ frac (1) (16)) + \ cdots) </Dd>

Limit of 1/2^n as n goes to infinity