Problem 649

Find the sum of the following infinite geometric series, if it exists.





S =\frac{ a}{1-r} , where r = common ratio (r ≤ 1) and a = first term.

a = \frac{2}{5}, r = \frac{6}{125}

S = \frac{\frac{2}{5}}{\left ( 1-\frac{6}{125} \right )}

S =\frac{ 50}{119}

So the sum of the infinite geometric series 50/119

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