_ r=1 ^ 20 (r^ 2 +1 )(r !) is equal to: - Vidyadip

MCQ

$\sum_{r=1}^{20}\left(r^{2}+1\right)(r !)$ is equal to:

A
$22\,!-21 !$
✓
$22\, !-2(21 \,!)$
C
$21\, !-2 (20\,!)$
D
$21 \,!-20\, !$

✓

Answer

Correct option: B.

$22\, !-2(21 \,!)$

b
$\sum_{x=1}^{20}\left(r^{2}+1\right) r !$

$\sum_{x=1}^{20}\left((r+1)^{2}-2 r\right) r !$

$\sum_{x=1}^{20}((r+1)(r+1) !-r \cdot r !)-\sum_{r=1}^{20} r \cdot r !$

$\sum_{x=1}^{20}((r+1)(r+1) !-r \cdot r !)-\sum_{r=1}^{20}((r+1) !-r !)$

$=(21.21-1)-(\lfloor 21-1)$

$=20.21 !=22 !-2 \cdot 21 !$

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