Question

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

Answer 1

Answer:

3

Step-by-step explanation:

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 3.

Answer 2

Answer:

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