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#.