How do you find the sum of the infinite geometric series 18-6+2-...?

1 Answer
Jan 11, 2016

27/2

Explanation:

We must write the general term of this alternating geometric series in the form ar^(n-1), where a is the first term and r is the common ratio between terms.

So in this case a=18 and r=-1/3.

Since |r|=1/3<1 it implies the series converges and the sum is given by a/(1-r).

therefore sum_(n=1)^oo18*(-1/3)^(n-1)=18/(1-(-1/3))=27/2.