Given p/q=1-(1/2)+(1/3)-(1/4)+...+(1/1317)-(1/1318)+(1/1319)
prove that p is divisible by 1979
p and q are natural numbers
a-math question~~~~~~~~~~
2009-03-04 6:32 am
回答 (1)
2009-03-04 6:50 am
✔ 最佳答案
1-(1/2)+(1/3)-(1/4)+...+(1/1317)-(1/1318)+(1/1319)=[1+(1/2)+...+(1/1319)]-2[(1/2+1/4+...+(1/1318)]
=(1/660+1/661+...+(1/1319)
=(1/660+1/1319)+(1/661+1/1318)+....+(1/989+1/990)
=1979[1/(660)(1319)+...+1/(989)(990)]
p is divisible by 1979
收錄日期: 2021-04-26 13:05:25
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