an expression is given below N = 1! + 2! +3! + 4! + 5! +………..99! + 100!. find the unit digit of N and find the last two digit of N and what will be the remainder when N is divided by 7

(Q). An expression is given below:
N = 1! + 2! + 3! + 4! + 5! + ………. + 99! + 100!
(i) Find the unit digit of N
(ii) Find the last two digit of N
(iii) What will be the remainder when N is divided by 7.

Solution:- 
(i)

Hence U𝒹 of N = 3 + 0 + 0 = 3 Answer

(ii) Last two digit of N = ?

Hence last two digit of N = 13 + 00
                                              = 13 Answer

(iii) Remainder when N is divided by 7 = ?

Since  ➜ R = 0
            ➜ R = 0

            ➜ R = 0
            ⋮
            ⋮
            ⋮

           ➜ R = 0
So final remainder will be
Remainder of 

= Remainder of 

= 5 Answer