Question

Sum of $1,-a,a^2,-a^3,...n$ terms (if $a\ne -1$).

Answer 1

Sum of $1,-a,a^2,-a^3....n$ terms

This is a G.P with A = 1; r = -a

$\{\frac{-a}{1}=-a\}$

$\therefore S_n=\frac{A(1-x^n)}{1-r}$

$\Rightarrow \frac{1(1-(-a{)}^n)}{1-(-a)}$

$S_n=\frac{1-(-a{)}^n}{1+a}$