1/5 + 1/5^2 + 1/5^3 + 1/5^4 = ?

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$\frac15+\frac1{5^2}+\frac1{5^3}+\frac1{5^4}=?$

A156/625

B165/625

C125/625

D135/625

Answer:

$L CM (5, 5^{2}, 5^{3}, 5^{4}) = 5^{4}$

$\frac{5 ^{4} \times \frac{1}{5} + 5 ^{4} \times \frac{1}{5 ^{2}} + 5 ^{4} \times \frac{1}{5 ^{3}} + 5 ^{4} \times \frac{1}{5 ^{4}}}{5 ^{4}}$

$\frac{5 ^{3} + 5 ^{2} + 5 ^{1} + 1}{5 ^{4}}$

$= \frac{125 + 25 + 5 + 1}{625}$

$= \frac{165}{625}$

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