1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算

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1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算
x)35767bC@vt7IZ<ݾ6IEj/FZ@XHh>jXD@%HX-\=0&PL kZalKK 10l}˅;m 4 5A v0lӾOc8=0[n4<

1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算
1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算

1-1/2+1/6+1/12+1/20+·········+1/72+1/90巧算
1-1/2+1/2*3+1/3*4+1/4*5……+1/8*9+1/9*10
=1-1/2+1/2-1/3+1/4-1/4+1/4-1/6+……+1/8-1/9+1/9-1/10
=1-1/10
=9/10

规律：每项=1/n(n+1)=1/n-1/(n+1)
原式=1-1/2+1/2-1/3+1/3-1/4+......+1/9-1/10=9/10