计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]

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计算1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]计算1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004

计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]
计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]

计算 1/[a(a+1)]+1/[(a+1)(a+2)]+……+1/[(a+2003)(a+2004)]
原式=1/a-1/(a+1)+1/(a+1)-1/(a+2)……+1/(a+2003)-1/(a+2004)
=1/a-1/(a+2004)
=2004/a(a+2004)

1/a(a+1)+.......=1/a-1/(a+1)+1/(a+1)-1/(a+2)+......+1/(a+2003)-1/(a+2004)=1/a-1/(a+2004)=2004/a(a+2004)