YLL討論網

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
=1/(659+1)+1/(659+2)+...+1/(659+330)+1/(1320-330)+1/(1320-329)+...+1/(1320-1)
=[1/(659+1)+1/(1320-1)]+...+[1/(659+330)+1/(1320-330)]
=1979/(660*1319)+1979/(661*1318)+...+1979/(989*990)
=1979*[1/(660*1319)+1/(661*1318)+...+1/(989*990)]
=(1979*k)/(660*661*...*1319)
=q/p，其中k是自然數
1979是質數，和660,661,...,1319無1以外的公因數

所以q是1979的倍數