Correct Answer - Option 1 : 0
Given:
Expression is 1! + 2! + 3! + 4! + 5! ......… + 95!
Calculation:
Here, given expression is 1! + 2! + 3! + 4! + 5! .........… + 95!
1! = 1
2! = 2 × 1 = 2
3! = 3 × 2 × 1 = 6
4! = 4 × 3 × 2 × 1 = 24
5! = 5 × 4 × 3 × 2 × 1 = 120
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
So, 6! It is divisible by 9.
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
So, 7! It is divisible by 9.
Similarly, every term greater than 6! In the given expression will be divisible by 9.
So, the sum of terms that are not divisible by 9 is
1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120 = 153
So, the remainder of 153 when divided by 9 will be 0.
∴ The remainder when 1! + 2! + 3! + … + 95! is divided by 9 is 0.
