find the remainder of the following when divided by 14.

Dear Student,

 

Note that in the given expression when divided by 14, all the terms from 7! onwards will be divided by 14 completely.

 

Therefore the remainder left will be the remainder left by the sum of the remainders left by 1!, 2!, 3!, 4!, 5! and 6! when divided by 14.

i.e. remainder left by 1! = 1

remainder left by 2! = 2

remainder left by 3! = 6

remainder left by 4! = 10

remainder left by 5! = 4

remainder left by 6! = 3

 

Total remainder is the remainder left by the sum of the remainders = 12

 

Regards Topperlearning.