Question

The value of 1+ 1.1! + 2.2! + 3.3! + .......... + n.n! is

• A. (n+1)!+1
• B. (n+1)!–1
• C. (n+1) !
• D. (n–1) !

Answer 1

The correct option is C (n+1) !

Required Sum = $1+{\sum }_{r=1}^{n}r(r!)$
= $1+{\sum }_{r=1}^n\left(\right(r+1)!-r!)$
= $1+(n+1)!-1=(n+1)!$