Yes, it converges

Calculus Level pending

\[\large 1 + \frac{3}{2!} + \frac{6}{3!} + \frac{10}{4!} + \cdots = \,? \]

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