# Q.17 $\quad$ Sum $\frac{1}{5}+\frac{1}{7}+\frac{1}{5^{2}}+\frac{1}{7^{2}}+\ldots .$ to $\infty=$ (A) $5 / 12$ (B) $3 / 4$ (C) $7 / 12$ (D) $3 / 49$

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Q.17 $\quad$ Sum $\frac{1}{5}+\frac{1}{7}+\frac{1}{5^{2}}+\frac{1}{7^{2}}+\ldots .$ to $\infty=$ (A) $5 / 12$ (B) $3 / 4$ (C) $7 / 12$ (D) $3 / 49$

$=\cfrac{\frac{1}{5}}{1-\frac{1}{5}}+\cfrac{\frac{1}{7}}{1-\frac{1}{7}}$ (∵ Sum of infinite series in G.P. when r < 1 is a/1-r)
$=\cfrac{\frac{1}{5}}{\frac{4}{5}}+\cfrac{\frac{1}{7}}{\frac{6}{7}}$
= 1/4 + 1/6 $=\frac{3+2}{12}$ = 5/12.