What is the sum of the following sequence:

1*1!, 2*2!, 3*3!, 4*4!, 5*5!......,99*99!

Thank you for help.

Guest Apr 25, 2017

#1**+1 **

Notice the pattern in the following sums:

1*1!+ 2*2!,+3*3! =23

1*1!+ 2*2!,+3*3! + 4*4! =119

1*1!+ 2*2!,+3*3! + 4*4! + 5*5! =719

Notice that the answer in each case is next number factorial - 1. In other words, the 23 is 4! - 1, and the 119 is 5! - 1, and the 719 is 6! - 1. And this pattern holds true for any sequence of such numbers.

Therefore, the sum of your sequence up to 99*99! = 100! - 1. This is the exact answer to your problem.

Guest Apr 26, 2017