SOLUTION: find sum of infinite series 1/2^n and series -1/2^n

Algebra ->  Sequences-and-series -> SOLUTION: find sum of infinite series 1/2^n and series -1/2^n      Log On


   

Question 758998: find sum of infinite series 1/2^n
and series -1/2^n
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The nth term of a geometric series is normally written a_n+=+a%2Ar%5E%28n-1%29
For this series, we know that the infinite sum S+=+a%2F%281-r%29
The series %281%2F2%29%5En has a=1 and r=1/2. This series has terms 1/2, 1/4, 1/8...
The series above has terms 1, 1/2, 1/4, 1/8...
So the two series differ by 1.
The sum of the series a_n+=+%281%2F2%29%5E%28n-1%29+=+1%2F%281-%281%2F2%29%29+=+2
Therefore the sum of the series a_n+=+%281%2F2%29%5En+=+2-1+=+1
I'll leave it to you to figure out the other one.