1 × 1! + 2 × 2! + 3 × 3! + 4 × 4! + ⋯ 10 × 10! = ?
Explanation:
T1 = 1 × 1! = (2 - 1) × 1! = 2 × 1! - 1 × 1! = 2! - 1!
T2 = 2 × 2! = (3 - 1) × 2! = 3 × 2! - 1 × 2! = 3! - 2!
T3 = 4! - 3!
... and so on.
∴ Let S = 1 × 1! + 2 × 2! + 3 × 3! + 4 × 4! + ⋯ 10 × 10!
⇒ S = (2! - 1!) + (3! - 2!) + (4! - 3!) + ... + (10! - 9!) + (11! - 10!)
⇒ S = 11! - 1! = 11! - 1
Hence, option (b).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.