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# Find the sum up to $n$ terms of the G.P. $1,-a,a^2,-a^3.........$

$\begin{array}{1 1}\large\frac{1-(A)^n}{1-a} \\ \large\frac{1-(-a)^n}{1+a} \\\large\frac{1-(-a)^n}{1-a} \\ \large\frac{1+(-a)^n}{1+a} \\ \large\frac{1+(-a)^n}{1+a} \end{array}$

Toolbox:
• Sum of $n$ terms of a G.P=$S_n=a.\large\frac{1-r^n}{1-r}$ where first term=$a$ and common ratio=$r$
Given G.P is $1,-a,a^2,-a^3........$
In this G.P first term$=a=1$ and common ratio $=r=-a$
We know that sum of $n$ terms of a G.P.$=a.\large\frac{1-r^n}{1-r}$
$\therefore \:S_n=1.\large\frac{1-(-a)^n}{1-r}$