Consider the following two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The sum of \(n\) terms of the Progression…

Consider the following two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) :

The sum of $n$ terms of the Progression

$1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+\cdots$ is $\frac{2^{n-1}-1}{2^{n-1}}$.

Reason (R) :

Sum of a geometric series having $n$ terms is given by $S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}$, where $a$ is the $1^{\text {st }}$ term and $r$ is the common ratio.