Sum of factorials

Number Theory Level 2

1 ! + 2 ! + 3 ! + ⋯ + 1000000000 ! \large 1!+2!+3!+\cdots+1000000000!

Find the last digit of the sum above.


Notation: ! ! is the factorial notation. For example, 8 ! = 1 × 2 × 3 × ⋯ × 8 8! = 1\times2\times3\times\cdots\times8 .


The answer is 3.

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Shikhar Gupta by Shikhar Gupta , 20, India

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1 solution

Phillip Temple
Mar 3, 2017

Anything greater than 4! will have at least one trailing 0, contributes nothing to the final digit, and is thus irrelevant, leaving 1!+2!+3!+4! mod 10 = 1+2+6+24 mod 10 = 3

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice, I solved it the same way.

Hana Wehbi - 4 years, 3 months ago

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