Question

Cat face 1+5^2+5^4+5^6+.....+5^58?

Answer 1

$\displaystyle S=1+5^2+5^4+5^6+...+5^{58}= \\ \\ ~~~=1+25+25^2+25^3+...+25^{29}= \\ \\ ~~~= \frac{25^{30}-1}{24}. \\ \\ Am~folosit~formula~1+a+a^2+...+a^n= \frac{a^{n+1}-1}{a-1},~pentru~ \\ \\ a \ne 1~si~faptul~ca~5^2=25.$