# Geometric series

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Determine if the following series converges and if possible give its sum

2/3 + 2/9 + 2/27 + 2/81 + ...

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Yes the series converges. It is an infinitie Geometric Series.

The series can be written as :

2/3 + (2/3)*1/3 + (2/3)*1/3^2 + (2/3)*1/3^3.......

The sum to an infinite Geometric series is given by :

a/(1-r) where a = first term

r = rate.

Putting in equation : a = 2/3 and r = 1/3 we have

2/3/(1-1/3)

= 2/3/(2/3)

= 1 ( Answer).

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