Question

Calculeaza g) 1/5+1/5^2+1/5^3

Answer 1

   
[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]