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Sequences and Series — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsSequences and Series1 Mark
Question
For the following G.P.s, find $S_n.: 0.7, 0.07, 0.007, …….$
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Answer

$a=0.7=\frac{7}{10}, r=\frac{0.07}{0.7}=\frac{1}{10}<1$
$S_n=\frac{a\left(1-r^n\right)}{1-r}, \text { for } r<1$
$=\frac{\frac{7}{10}\left[1-\left(\frac{1}{10}\right)^n\right]}{1-\frac{1}{10}}=\frac{7}{9}\left(1-\frac{1}{10^n}\right)$

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