JEE Mains · Maths · STD 11 - 8. sequence and series
\(\sum_{r=1}^{20}\left(r^{2}+1\right)(r !)\) is equal to:
- A \(22\,!-21 !\)
- B \(22\, !-2(21 \,!)\)
- C \(21\, !-2 (20\,!)\)
- D \(21 \,!-20\, !\)
Answer & Solution
Correct Answer
(B) \(22\, !-2(21 \,!)\)
Step-by-step Solution
Detailed explanation
\(\sum_{x=1}^{20}\left(r^{2}+1\right) r !\) \(\sum_{x=1}^{20}\left((r+1)^{2}-2 r\right) r !\) \(\sum_{x=1}^{20}((r+1)(r+1) !-r \cdot r !)-\sum_{r=1}^{20} r \cdot r !\) \(\sum_{x=1}^{20}((r+1)(r+1) !-r \cdot r !)-\sum_{r=1}^{20}((r+1) !-r !)\) \(=(21.21-1)-(\lfloor 21-1)\)…
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