General
What does ½ + ¼ + ⅛ + … add up to forever?
What is the sum of the infinite geometric series: ½ + ¼ + ⅛ + 1/16 + …?
People also ask
What is the answer to the infinite series ½ + ¼ + ⅛ + 1/16 + … ?
The answer is 1. As you keep halving and adding the pieces forever, the total gets closer and closer to exactly 1 and never goes past it.
How do you find the sum of an infinite geometric series?
Use the formula a ÷ (1 − r), where a is the first term and r is the common ratio with |r| < 1. Here a = ½ and r = ½, so ½ ÷ (1 − ½) = 1.
Why doesn't adding infinitely many numbers give infinity?
Because each term is much smaller than the last. When the ratio is below 1, the pieces shrink fast enough that the total converges to a finite number instead of growing without bound.