What is the remainder when 1! + 2! + 3! + ... + 100! is divided by 30?

Question

legomyego180 · Answer

Hm.

$$\sum_{n=1}^{100} n!$$

Are you learning taylor and mclaurin series?

kkrocks2 · Answer

@legomyego180 No, I'm learning about modular arithmetic and modular arithmetic sums.

legomyego180 · Answer

Oh woah, way above my head. Sorry

legomyego180 · Answer

Looks interesting though

kkrocks2 · Answer

@legomyego180 haha it's okay, I know it's a really tough problem bc it's a really tough course... I got everything else on my forum page but I can't figure out this one

rishabh.mission · Answer

Try solving it using https://www.quora.com/What-is-the-remainder-when-1-+2-+3-+4-+100-is-divided-by-24

math&ing001 · Answer

What @rishabh.mission wrote makes sense.
Everything above 5! will have a reminder of 0, so only count the reminders for 1!, 2!, 3!, and 4!

kkrocks2 · Answer

@rishabh.mission @math&ing001 
that makes so much sense! I understand that the remainders will be 1!, 2!, 3!, and 4! but the total of that is 33 which is greater than 30? Does this mean the remainder is 3?

math&ing001 · Answer

Yep !

rishabh.mission · Answer

yes.

kkrocks2 · Answer

@math&ing001 @rishabh.mission thank u both so much

math&ing001 · Answer

Welcome :)

rishabh.mission · Answer

:) YW