Can anyone pl try to solve the following problem:

What is the reminder when ( 1!+2!+3!+.....+95! ) is divided by 15 ?

I could not apply reminder theorm or Patten method to the above sum.

Thank you,
Suresh

There is no try. Do!

>What is the reminder when ( 1!+2!+3!+.....+95! ) is divided
>by 15 ?
>
>I could not apply reminder theorm or Patten method to the
>above sum.

I am not sure about what are those, but you may want to note that, for some sufficiently large n, n! is divisible by 15. I am certain that 95! has this property, and so does 94!, and also 93!, etc. You should think of the smallest number with that property.

Well Suresh, Let us write the sum as follows -
S = 1! + 2! + 3! + 4! + X;
Note now that X is divisible by 15 (Always !!!) becoz each n! term in X when written down as a product 1*2*3*4*5*...*n can be seen to have 3 and 5 in the product :o)
So the reminder must be 3. What say?

take care