MathDB

Infinate Geometric Series

Source:

November 13, 2005

ratiogeometric seriesnumber theoryrelatively primealgebrasystem of equations

Problem Statement

An infinite geometric series has sum

2005

. A new series, obtained by squaring each term of the original series, has

10

times the sum of the original series. The common ratio of the original series is

\frac{m}{n}

where

m

and

n

are relatively prime integers. Find

m+n