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The sum to infinity of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + \dots$ is

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Correct option is C

S=1+45+752+1053+… (1)15S=15+452+753+… (2)Subtracting (2) from (1), we get 45S=1+35+352+353+…=1+3/51−1/5(1) =1+34=74 (2)⇒ S=3516

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The sum to infinity of the series 1+45+752+1053+… is

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The sum to infinity of the series $1 + \frac{4}{5} + \frac{7}{5^{2}} + \frac{10}{5^{3}} + \dots$ is