What is the sum of the following sequence:
1*1!, 2*2!, 3*3!, 4*4!, 5*5!......,99*99!
Thank you for help.
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.
