Question

How do you find the sum of the infinite geometric series `Sigma (1/2)^n` from n=0 to `oo`?

Answer 1

The sum is 2.

Explanation:

Realize that the sum of a geometric series of the form `sum ar^n` can be represented by `a/(1-r)` where `a` is the first term of the series and `r` is the common ratio. Thus we can see that the series `sum (1/2)^n` is of the form of a geometric series, where the r is 0.5 and the a is 1.

So the sum of our series becomes `1/(1-(1/2))` which is `1/0.5 = 2`