Question

The sum ${\sum }_{k=1}^{10}$ k.k! equals

• A. (10)!
• B. (11)!
• C. (10)! + 1
• D. (11)! - 1

Answer 1

The correct option is D (11)! - 1

${\sum }_{k=1}^{10}k.k!=1.1!+2.2!+3.3!+.....10.10!$

First term can be written as difference of $1$.

$=(2-1)!+(3-1)2!+(4-1)3!+......(11-1)10!=2!-1!+3!-2!+4!-3!+.......11!-10!$

only two terms are left $=11!-1$