# Math Help - Quickie #6

1. ## Quickie #6

Find the sum of the series:

. . $1(1!) + 2(2!) + 3(3!) + \cdots + n(n!)$

2. Originally Posted by Soroban
Find the sum of the series:

. . $1(1!) + 2(2!) + 3(3!) + \cdots + n(n!)$
(n+1)!-1

It is just mathematical iduction

3. I don't know where it was solved, but even without (explicit) induction:

$
k\left( {k!} \right) = \left( {k + 1} \right)k! - k! = \left( {k + 1} \right)! - k!
$

So summing for k = 1 till n gives (n+1)!-1 since all intermediate terms cancel out.