Factorial

[shrey2287]

Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

(1) n! +1
(2) (n+1)!
(3) (n+1)!-1
(4) (n+1)!+1
(5) None of these

[ehsansystem]

Plugged in some numbers .... But I could not find any logical shortcut ...
But the answer is C

[Anurag@Gurome]

Find the value of 1.1! + 2.2! + 3.3! + ......+n.n!

Algebraic Approach:
1.1! = 2.1! - 1! = 2! - 1!
2.2! = 3.2! - 2! = 3! - 2!
3.3! = 4.3! - 3! = 4! - 3!
...
n.n! = (n + 1).n! - n! = (n + 1)! - n!

Now note that if we sum up the expanded expressions alternate terms will cancel each other except the -1! and (n + 1)!.

Hence, sum of the expression = (n + 1)! - 1

The correct answer is C.