Question

Find the sum to indicated number of terms in each of the geometric progressions in$x^3,x^5,x^7$, ... n terms (if x ≠ ± 1).

Answer 1

The given G.P. is $x^3,x^5,x^7$, ...

Here, a = $x^3$ and r = $x^2$

Sn = a$\frac{(1-r^n)}{1-r}$

= $\frac{x^3[1-(x^2)^n]}{1-x^2}$

= $\frac{x^3(1-x^2n)}{1-x^2}$