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  4. The value of 1 + 1.1! + 2.2! + 3.3! + ... + n.n!

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Q. The value of $1 + 1.1! + 2.2! + 3.3! + ... + n.n!$

Permutations and Combinations

Solution:

n . n! = [(n+1) -1] n! = (n+1)! - n!
$\therefore $ 1+ 2! - 1! + ... + (n + 1)! - n! = (n + 1)!