What is the sum of the infinite geometric series #sum_(n=1)^oo2^n/5^(n-1)# ?

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What is the sum of the infinite geometric series #sum_(n=1)^oo2^n/5^(n-1)# ?

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Answer 1 · 2014-07-23T21:47:19

This series can be rewritten as #sum_{n=1}^\infty 2(2/5)^{n-1}# and is thus a geometric series with first term 2 and common ratio #2/5#. Since the common ratio is less than 1 (in absolute value), the series is convergent and its sum is given by #"first term"/(1-"common ratio")=2/(1-2/5)=10/3#. See Geometric Series

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What is the sum of the infinite geometric series #sum_(n=1)^oo2^n/5^(n-1)# ?

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