JIPMAT (QA) PYQs

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.

The value of $(\frac{1}{\sqrt{9}-\sqrt{8}} - \frac{1}{\sqrt{8}-\sqrt{7}} + \frac{1}{\sqrt{7}-\sqrt{6}} - \frac{1}{\sqrt{6}-\sqrt{5}} + \frac{1}{\sqrt{5}-\sqrt{4}})$ is