1990/1*2+1990/2*3+1990/3*4+...+1990/1988*1989+1900/1989*1990

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1990/1*2+1990/2*3+1990/3*4+...+1990/1988*1989+1900/1989*1990
1990/1*2+1990/2*3+1990/3*4+...+1990/1988*1989+1900/1989*1990

1990/1*2+1990/2*3+1990/3*4+...+1990/1988*1989+1900/1989*1990
原式=1990/1 -1990/2 +1990/2 - 1990/3…… +1990/1989-1990/1990
=1990/1 - 1990/1990
=1990-1
=1989
分析:a/[n× (n+1)]=a/n - a/(n+1),例如1990/(1×2)=1990/1 - 1990/2
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