อ้างอิง:
ข้อความเดิมเขียนโดยคุณ gnap
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ลองดูข้อ1. IMO ปี1979 ดูครับ
Problem A1
m/n = 1 - 1/2 + 1/3 - 1/4 + ... - 1/1318 + 1/1319.
Prove that m is divisible by 1979.
Solution
1 - 1/2 + 1/3 - 1/4 + ... - 1/1318 + 1/1319
= 1 + 1/2 + 1/3 + ... + 1/1319 - 2(1/2 + 1/4 + ... + 1/1318)
= 1 + 1/2 + 1/3 + ... + 1/1319 - (1+1/2+1/3+...+1/659)
= 1/660 + 1/661 + ... + 1/1319.
and to notice that 660 + 1319 = 1979. Combine terms in pairs from the outside:
1/660 + 1/1319 = 1979/(660.1319);
1/661 + 1/1318 = 1979/(661.1318) etc.