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\(\frac{(1-r^n)}{1-r}\)

= \(\frac{x^3[1-(x^2)^n]}{1-x^2}\)

= \(\frac{x^3(1-x^2n)}{1-x^2}\)