Question

Find the remainder when 1! + 2! +3! + .. .. .. .. +100! is divided by
15
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Answer 1

Answer:

First just expand some of the starting factorials.

1! = 1 x 1

2! = 2 x 1

3! = 3 x 2 x 1

4! = 4 x 3 x 2 x 1

5! = 5 x 4 x 3 x 2 x 1, So it is clearly visible that 5! is a multiple of 15 as it contains 5 and 3 in its expansion, so if we divide 5! by 15 the remainder will be zero.

And from now on all the upcoming factorials will be a multiple of 15, as

6! = 6 x 5!

7! = 7 x 6 x 5!

...

...

...

So, the factorial which will affect the remainder are,

1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33

So, when 33 is divided by 15 the remainder is three.

So, the answer must be 3.

I hope my solution was helpful.

Thank you.

Step-by-step explanation:

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