Telescoping the Reciprocals!

Algebra Level 4

$\begin{aligned} \frac{3}{1!+2!+3!} + \frac{4}{2!+3!+4!} + \frac{5}{3!+4!+5!} + \cdots+ \frac{100}{98!+99!+100!} \end{aligned}$

Find the value of the expression above.

The answer is a form of $\frac{1}{a!} - \frac{1}{b!}$ . Submit your answer as $a \times b$ .

Notation: $!$ is the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .