Question

The value of \(\frac{C(n,2){(n+1)!}\) is}

• A. \(\frac{1}{2}e + 1\)
• B. \(e + 1\)
• C. \(\frac{1}{2}e - 1\)
• D. \(e\)

Hint:

Convert factorial expressions to match \(e^x\) series.

Answer 1

The Correct Option is C

Concept: \[ \sum \frac{n(n-1)}{2(n+1)!} \]

Step 1: Rewrite.
\[ = \frac{1}{2}\sum \frac{n(n-1)}{(n+1)!} \]

Step 2: Simplify factorial.
\[ = \frac{1}{2}(e -2) \] \[ = \frac{1}{2}e -1 \]