Question
Sat August 11, 2012 By:
 

Find the sum up to n terms: 1.1!+2.2!+3.3!+........+n.n!

Expert Reply
Sat August 11, 2012
We have:
a*a! = (a+1 - 1)*a! = (a+1)a! - a! = (a+1)! - a! 

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

                                              = -1! + (n+1)! or (n+1)! - 1 
Home Work Help