displaystyle∑r=120(r2+1)(r !) is equal to:

Question

displaystyle∑r=120(r2+1)(r !) is equal to: (A) 22 !-21 ! (B) 22 !-2(21 !) (C) 21 !-2(20 !) (D) 21 !-20 !

Tardigrade Admin · Accepted Answer

displaystyle ∑x=120(r2+1) r ! displaystyle∑x=120((r+1)2-2 r) r ! displaystyle∑x=120((r+1)(r+1) !-r ⋅ r !)- displaystyle∑r=120 r ⋅ r ! displaystyle∑x=120((r+1)(r+1) !-r ⋅ r !)- displaystyle∑r=120((r+1) !-r !) =(21 ⋅ angle21-1)- angle 21-1) =20.21 !=22 !-2.21 !

Q. $r = 1 \sum 20 (r^{2} + 1) (r!)$ is equal to:

$22! - 21!$

$22! - 2 (21!)$

$21! - 2 (20!)$

$21! - 20$ !

$x = 1 \sum 20 (r^{2} + 1) r!$
$x = 1 \sum 20 ((r + 1)^{2} - 2 r) r!$
$x = 1 \sum 20 ((r + 1) (r + 1)! - r \cdot r!) - r = 1 \sum 20 r \cdot r!$
$x = 1 \sum 20 ((r + 1) (r + 1)! - r \cdot r!) - r = 1 \sum 20 ((r + 1)! - r!)$
$= (21 \cdot ∠ 21 - 1) - {∠ 21 - 1)$
$= 20.21! = 22! - 2.21!$

Q. r=1∑20​(r2+1)(r!) is equal to:

22!−21!

22!−2(21!)

21!−2(20!)

21!−20 !