1/1x3+1/2x4+1/3x5+...+1/9X11=?

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1/1x3+1/2x4+1/3x5+...+1/9X11=?

1/1x3+1/2x4+1/3x5+...+1/9X11=?
1/1x3+1/2x4+1/3x5+...+1/9X11=?

1/1x3+1/2x4+1/3x5+...+1/9X11=?
因为1/n(n+2)=[1/n-1/(n+2)]/2
所以1/1*3+1/2*4+1/3*5+...+1/9*11
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/9-1/11)]/2
=(1+1/2-1/10-1/11)/2
=36/55

原式=1/2(1-1/3+1/2-1/4+1/3-1/5…+1/9-1/11)
=1/2(1+1/2-1/10-1/11)
=36/55

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