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Q.
The sum of the infinite series $\frac{3}{11}+\frac{33}{11^2}+\frac{333}{11^3}+\ldots \ldots$ is
Sequences and Series
Solution:
$ S =\frac{3}{11}+\frac{33}{11^2}+\frac{333}{11^3}+\ldots \ldots$
$\frac{ S }{11}=\frac{3}{11^2}+\frac{33}{11^3}+\ldots \ldots$
$\frac{10}{11} S =\frac{3}{11}+\frac{30}{11^2}+\frac{300}{11^3}+\ldots . . $
$\Rightarrow S =\frac{11}{10} \times \frac{\frac{3}{11}}{1-\frac{10}{11}}=\frac{33}{10}$