# Thread: what is the remainder of the summation when divided by ten

1. ## what is the remainder of the summation when divided by ten

I got this question in a maths competition. the question was that what was the remainder of the equation given below when divided by 10.

$\sum_{n=1}^{10} (n^2+3n+1)n!$

i personally do not what to do with the n!
im lost

2. Hee swanz,

Do you know how to do modulo-calculations? That is, how to add and multiply residu-classes modulo 10?

This problem is actually quite simple if you can do this and make one simple observation. Namely, $n!\equiv 0$ mod 10 for all $n\geq 5$

3. Start by noting that for any $n \geq 5, ~ n! \equiv 0 ~ (mod 10)$.

Ah, Dinkydoe got to it before I did... !

4. no i am in kindda in high school still lol
sorry =/ but u can tell me whateva i need to learn to solve this thereby i can learn some of it online,
yes i knw n! mod 10 = 0
yes i did make that observation that n! in mod 10 is 0 for all values of n more than equal to 5...but still lost :L

5. sorry ....i got it :L ...
$\sum_{n=1}^{10}(n^2+3n+1)n!$ has the same remainder as $\sum_{n=1}^{4}(n^2+3n+1)n!$ when divided by 10