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

1 Answer
Mar 27, 2017

Answer:

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#