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Thus for every integer n larger than 4, n! is a multiple of 10 and hence has a units digit of 0. Thus the units digit of 0! + 1! + 2! + 3! + 4! .............+9999! + 10000! is the units digit of the sum 0! + 1! + 2! + 3! + 4! = 1 + 1 + 2 + 6 + 24 = 34. Hence the units digit of 0! + 1! + 2! + 3! + 4! .............+9999! + 10000! is 4. I hope this helps,
Work out (say) the first twelve factorials. You may use a calculator, but should do it by multiplying each factorial by the next natural number: as, 1x2 = 2, 2x3 = 6, 6x4 = 24, 24 x 5 = 120. You should already see a pattern; if not, compute the sums 0! = 1 1 + 1 = 2 and you will surely see the pattern that will let you answer the question. Good Hunting!  


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