Last digit

Number Theory Level 2

Find the last digit.

100 ! + 99 ! + 98 ! + . . . + 3 ! + 2 ! + 1 ! + 0 ! \large{100!+99!+98!+...+3!+2!+1!+0!}

1 4 5 0 3

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1 solution

Starting form 5 ! 5! to 100 ! 100! , the last digit is 0 0 because of the factors 2 × 5 2 \times 5 which is equal to 10 10 and ends with 0 0 .

So

0 ! + 1 ! + 2 ! + 3 ! + 4 ! = 1 + 1 + 2 + 6 + 24 = 34 0!+1!+2!+3!+4!=1+1+2+6+24=34

The answer is 4 \color{#D61F06}\boxed{4} .

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