解：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)+(1/4-1/4)+...+(1/9-1/9)-1/10
=1+0+0+0+...+0-1/10
=1-1/10
=9/10
1/1*2+1/2*3+1/3*4+......+1/9*10
=(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
1—1/2+1/2—1/3+1/3—1/4+........+1/9-1/10
=1-1/10
=9/10
1/(1*2)+1/(2*3)+1/(3*4)+......+1/(9*10)
=1-1/2+1/2-1/3+1/3-1/4+......+1/9-1/10
=1-1/10
=9/10
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