JIPMAT 2021 (QA) PYQs

Given below are 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

$1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+$ 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.

The sum of $n-$ terms of sequence $\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4} \ldots \ldots$. Is

Assertion [A]: Sum of the first hundred even natural numbers divisible by 5 is 45050.
Reason (R): Sum of the first n-terms of an Arithmetic Progression is given by $S = (n/2) *(a + l)$ where a=first term, l=last term.
Choose the correct answer from the options given below.