find-the-value-of-2-1-4-2-6-3-200-100-

Question Number 155802 by cortano last updated on 05/Oct/21

find the value of

2 \times 1! + 4 \times 2! + 6 \times 3! + \dots + 200 \times 100!

Answered by talminator2856791 last updated on 05/Oct/21

use the information in the post

above this post Q . 155803 :

\underset{k = 1}{\sum^{n}} k \times k! = (n + 1)! - 1

2 \times 1! + 4 \times 2! + \dots . . + 200 \times 100!

= 2 (1 + 1! + 2 \times 2! + \dots . . + 100 \times 100!)

= 2 \underset{k = 1}{\sum^{100}} k \times k!

= 2 ((100 + 1)! - 1)

= \begin{matrix} 2 \times 101! - 2 \end{matrix}