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Numbers and Sequences — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSNumbers and Sequences2 Marks
Question
Find the sum to infinity of 9 + 3 + 1 + ….
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Answer

$\begin{aligned} & 9+3+1+\ldots . \\ & a=9, r=\frac{3}{9}=\frac{1}{3}<1 \\ & S_{\infty}=\frac{a}{1-r} \\ & =\frac{9}{1-\frac{1}{3}} \\ & =\frac{\frac{9}{3-1}}{3} \\ & =\frac{\frac{9}{2}}{3} \\ & =9 \times \frac{3}{2} \\ & =\frac{27}{2}\end{aligned}$

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