Question

The remainder when 1!+2!+3!+...99! is divided by 15 is​

Answer 1

Answer:

Note that 5!=1⋅2⋅3⋅4⋅5 is divisible by 15, and hence for any number, n≥5, we have n!=1⋅2⋅3⋅4⋅5⋯n is divisible by 15.

Therefore the remainder when 1!+2!+⋯+95! is divided by 15 is same as the remainder when 15 divides 1!+2!+3!+4!. 

Now, 1!+2!+3!+4!=1+2+6+24=33 is divided by 15, then the remainder is