1\1x2+1\2x3+1\3x4+……+1\10x11

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1\1x2+1\2x3+1\3x4+……+1\10x111\1x2+1\2x3+1\3x4+……+1\10x111\1x2+1\2x3+1\3x4+……+1\10x111\1x2+1\2x3+1\3x

1\1x2+1\2x3+1\3x4+……+1\10x11
1\1x2+1\2x3+1\3x4+……+1\10x11

1\1x2+1\2x3+1\3x4+……+1\10x11
1\1x2+1\2x3+1\3x4+……+1\10x11
=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11
=1-1/11
=10/11

1\1x2+1\2x3+1\3x4+……+1\10x11
=1-1/2+1/2-1/3+1/3-1/4.....+1/10-1/11
=1-1/11
=10/11

原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/10-1/11)
=1-1/11=10/11