Question

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

• A. 156/625
• B. 165/625
• C. 125/625
• D. 135/625

Answer 1

Answer:

A. 156/625

$LCM(5,5^2,5^3,5^4)=5^4$

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

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

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

$=\frac{165}{625}$