1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算

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1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算

1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算
1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算

1/1x2+1/2x3+1/3x4+1/4x5.1/9x10简算
由裂项公式:1/[n(n+1)]=1/n-1/(n+1)知:
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/9-1/10)
=1-1/2+1/2-1/3+1/3-1/4……+1/9-1/10
=1-1/10
=9/10

原式=1-1/2+1/2-1/3+1/3-1/4……+1/9-1/10=1-1/10=9/10

1/1*2=1-1/21/2*3=1/2-1/3...1/9*10=1/9-1/10等式两边相加得/1x2+1/2x3+1/3x4+1/4x5+……+1/9x10=1-1/10=9/10