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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