Question

Find the remainder when 1!+2!+3!+4!+5!+....+49! is divided by 7

Answer 1

Heya user, 

Clearly , 7 | x! [ if 'x' > 7 ]

Hence our req.d remainder is 1! + 2! + ... + 6! (mod 7) 
Let remainder = r..

Then r ≡ 1 + 2 + 6 + 24 + 120 + 720 (mod 7) ≡ 1 + 2 -1 + 3 + 1 -1 (mod7)
.'. r ≡ 2 + 3 (mod7) = 5 (mod7)

Hence, our remainder is 5.......

Answer 2

5 will be remainder.

1+2+3+4+5+6+49/7