Question

The value of ${\sum }_{r=1}^{10}r{.}^r{P}_r$ =

• A. 11!
• B. 11! - 1
• C. 11! + 1
• D. 11! - 11

Answer 1

The correct option is B 11! - 1

${\sum }_{r=1}^{10}r{.}^r{P}_r={\sum }_{r=1}^{10}(r+1-1)r!$ $={\sum }_{r=1}^{10}\left(\right(r+1)!-r!)=11!-1!=11!-1$