Question

Sum of the series, $x^3,x^5,x^7,...nterms(ifx\ne \pm 1).$

Answer 1

The given G.P. is $x^3,x^5,x^7........$
Here,$a=x^3$ and $r=x^2$
$\therefore S_n=\frac{a(1-r^n)}{1-r}=\frac{x^3[1-(x^2{)}^n]}{1-x^2}=\frac{x^3[1-(x^{2n}]}{1-x^2}$