Question

The last digit of $\sum _{1<p<100}p!-\sum _{n=1}^{50}\left(2n\right)!$ where $p$ is a prime number

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (C)

$6$

The sum is,

$2!+3!+4!+5!.....-(2!+4!+6!...)$

After $5!$ the number will have $0$ at the one's place, so they will no effect the last digit of the total sum,

Now last digit of $2!=2,3!=6,4!=4$

So, the last digit will be $2+6+4-2-4=6$