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Q.
The sum to infinity of the series $1+\frac{4}{5}+\frac{7}{5^{2}}+\frac{10}{5^{3}}+\ldots $ is
NTA AbhyasNTA Abhyas 2022
Solution:
$S=1+\frac{4}{5}+\frac{7}{5^{2}}+\frac{10}{5^{3}}+\ldots +\infty$ ... (1)
$\frac{S}{5}=0+\frac{1}{5}+\frac{4}{5^{2}}+\frac{7}{5^{3}}+\ldots +\infty$ ... (2)
On subtracting both the eq (1) and (2), we get,
$\frac{4}{5}S=1+\frac{3}{5}+\frac{3}{5^{2}}+\ldots +\infty$
$S=\frac{35}{16}$