+0  
 
0
57
2
avatar

Find the last two digits of the following sum: $$5! + 6! + 7! + 8! + \cdots + 100!$$

 Jul 30, 2021
 #1
avatar+58 
-5

to solve this problem, adding everything together would be far too slow.

 

As a faster solution, I suggest figuring out the last two digits for every value and finding a pattern.

 

5! = 120

6! = 720

7! = 5040

8! = 30240

9! = 362880

10! = 3628800

11! = 39916800

and as we can observe, all the rest all ends in 00

 

the answer: 20+20+40+80= 160, and we want the last two digits, which are 60

 Jul 30, 2021
 #2
avatar
0

sumfor(n, 5, 100, n!)==94269001 6837099792 6085983412 4473539872 0707226139 8267244293 8359305624 6782234795 0602340029 4093599136 4669866091 2434743264 7622826870 0382205564 4233652892 0420940280

 

The last 2 digits ==80

 Jul 30, 2021

26 Online Users

avatar
avatar