The sum of (12 – 1 + 1)(1!) + (22 – 2 + 1)(2!) + …. + (n2 – n

1.	The sum of (12 – 1 + 1)(1!) + (22 – 2 + 1)(2!) + …. + (n2 – n + 1)(n!) is - (A) (n + 2)! (B) (n – 1)((n + 1)!) + 1 (C) (n + 2)! – 1 (D) n((n + 1)!) – 1
Answer» Correct Option :- (B) (n – 1)((n + 1)!) + 1 Explanation :- T_n = (n² – n + 1) n! = (n² – 1) n! – (n – 2) n! T_n = (n – 1) (n + 1) ! – (n – 2) n! Sum = 1 + (n – 1) (n + 1) !

The sum of (12 – 1 + 1)(1!) + (22 – 2 + 1)(2!) + …. + (n2 – n + 1)(n!) is - (A) (n + 2)! (B) (n – 1)((n + 1)!) + 1 (C) (n + 2)! – 1 (D) n((n + 1)!) – 1

Answer»

Correct Option :- (B) (n – 1)((n + 1)!) + 1

Explanation :-

T_n = (n² – n + 1) n!

= (n² – 1) n! – (n – 2) n!

T_n = (n – 1) (n + 1) ! – (n – 2) n!

Sum = 1 + (n – 1) (n + 1) !

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The sum of (12 – 1 + 1)(1!) + (22 – 2 + 1)(2!) + …. + (n2 – n + 1)(n!) is - (A) (n + 2)! (B) (n – 1)((n + 1)!) + 1 (C) (n + 2)! – 1 (D) n((n + 1)!) – 1

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