Question 1184226
.
<pre>

The formula is


    1*1! + 2*2! + 3*3! + . . . + n*n! = (n+1)! - 1.


For the proof (quite easy) see this link


https://www.quora.com/What-is-the-sum-of-1-1-2-2-3-3-n-n
</pre>