Question

Find the sum to $n$ terms of G.P., $x^3,x^5,x^7...$ (if $x\ne \pm 1$)

Answer 1

Given, $x^3,x^5,x^7....$ are in G.P.
Here, first term $=a=x^3$ and common ratio $=r=\frac{x^5}{x^3}=x^2$
We know, the sum of $n$ terms of G.P. is
$S_n=\frac{a(1-r^n)}{1-r}$
$\Rightarrow S_n=\frac{x^3[1-(x^2{)}^n]}{1-x^2}$
$\therefore S_n=\frac{x^3(1-x^{2n})}{1-x^2}$