Question

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

Answer 1

`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`.