Find the sum to n terms in the geometric progression


Find the sum to n terms in the geometric progression $1,-a, a^{2},-a^{3} \ldots($ if $a \neq-1)$


The given G.P. is $1,-a, a^{2},-a^{3}, \ldots \ldots \ldots \ldots . .$

Here, first term $=a_{1}=1$

Common ratio $=r=-a$


$\therefore S_{n}=\frac{1\left[1-(-a)^{n}\right]}{1-(-a)}=\frac{\left[1-(-a)^{n}\right]}{1+a}$

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