Problem 649

Sir SagarMarch 18, 20150

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

$\frac{2}{5}+\frac{12}{25}+\frac{72}{125}+...$

Solution:-

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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