7th Iberoamerican 1992 Problem A1 a n is the last digit of 1 + 2 + ... + n. Find a 1 + a 2 + ... + a 1992 .
It is easy to compile the following table, from which we see that a n is periodic with period 20, and indeed the sum for each decade (from 0 to 9) is 35. Thus the sum for 1992 is 199·35 + 5 + 6 + 8 = 6984. n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a n 0 1 3 6 0 5 1 8 6 5 5 6 8 1 5 0 6 3 1 0 0 sum 0 1 4 10 10 15 16 24 30 35 40 46 54 55 60 60 66 69 70 70 70 7th Ibero 1992 © John Scholes jscholes@kalva.demon.co.uk 11 July 2002