The Bizzarre Digits
Number Theory
Level
pending
Find last two digits of(1!+2!+3!+...+1997!)
The answer is 13.
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1 solution
Let S = 1!+2!+3!+...+1997! From 5! all the numbers will have unit digit 0 and 1! +2!+3!+4! = 33 Thus unit digit is 3 Now from 10! all digits will have unit and ten's digit zero and 1!+2!+..+9!=33+120+720+5040+...+362880 So to get ten's digit add only the ten's digit of given series whcih is 3+2+2+4+2+8=21 ten's digit is 1 Therfore solution is 13