What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . . n × n!
where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1

A. n × (n - 1) × (n - 1)!

B. (n + 1)! - {n × (n - 1)}

C. (n + 1)! - n!

D. (n + 1)! - 1!

Answer: Option D

Solution(By Examveda Team)

1 × 1! = (2 - 1) × 81! = 2 × 1! - 1 × 1! = 2! - 1!
2 × 2! = (3 - 1) × 2! = 3 × 2! - 2! = 3! - 2!
3 × 3! = (4 - 1) × 3! = 4 × 3! - 3! = 4! - 3!
..
..
..
n × n! = (n + 1 - 1) × n! = (n + 1) (n!) - n! = (n + 1)! - n!
Summing up all these terms, we get (n + 1)! - 1!