[tex]\displaystyle \bf\\
\frac{1}{5} +\frac{1}{5^2} +\frac{1}{5^3} = \\\\
= \frac{1\times 5^2}{5\times 5^2} +\frac{1\times 5}{5^2\times 5} +\frac{1}{5^3} = \\\\
= \frac{5^2}{5^3} +\frac{5}{5^3} +\frac{1}{5^3} = \\\\
= \frac{5^2+5+1}{5^3} =\frac{25+5+1}{5^3} =\boxed{\bf \frac{31}{5^3}}=\boxed{\bf \frac{31}{125}}[/tex]
