How does the sum of 1/2 + 1/4 + 1/8 etc. (Halves each time) eventually become 1? I understand it’s infinite but surely it still wouldn’t work?
In: Mathematics
In this case, it’s easy to evaluate the infinite series.
S = 1/2 + 1/4 + 1/8 + …
Multiply both sides of the equation by 2:
2S = 2/2 + 2/4 + 2/8 + …
2S = 1 + 1/2 + 1/4 + 1/8 + …
So
2S = 1 + S
Subtract S from both sides, and
S = 1.
Latest Answers