Question

The value of $1.1!+2.2!+3.3!+..........+n.n!,$ is

• A. $(n+1)!$
• B. $(n+1)!+1$
• C. $(n+1)!-1$
• D. None of these

Answer 1

The correct option is C $(n+1)!-1$

$S=1.1!+2.2!.......................n.n!$

$=(2-1)1!+(3-1)2!....................(n+1-1)n!$

$=2.1!-1.1!+3.2!-2!................(n+1)n!-n!$

$=2!-1!+3!-2!.........................(n+1)n!-n!$

$=(n+1)!-1$