1. ## Quickie #6

Find the sum of the series:

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

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

. . $\displaystyle 1(1!) + 2(2!) + 3(3!) + \cdots + n(n!)$
$\displaystyle k\left( {k!} \right) = \left( {k + 1} \right)k! - k! = \left( {k + 1} \right)! - k!$