x(x+1)分之1+(x+1)(x+2)分之一+(x+2)(x+3)分之一+...+(x+1998)(x+1999)分之一等于多少?
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x(x+1)分之1+(x+1)(x+2)分之一+(x+2)(x+3)分之一+...+(x+1998)(x+1999)分之一等于多少?
x(x+1)分之1+(x+1)(x+2)分之一+(x+2)(x+3)分之一+...+(x+1998)(x+1999)分之一等于多少?
x(x+1)分之1+(x+1)(x+2)分之一+(x+2)(x+3)分之一+...+(x+1998)(x+1999)分之一等于多少?
1/x(x+1)=1/x-1/(x+1)
1/(x+1)(x+2)=1/(x+1)-1/(x+2)
后面以此类推
原式=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+1998)-1/(x-1999)
=1/x-1/(x-1999)
=1999/x(x-1999)
x(x+1)分之1+(x+1)(x+2)分之一+(x+2)(x+3)分之一+...+(x+1998)(x+1999)分之一
=[1/x-1/(x+1)]+[1/(x+1)-1/(x+2)]+...[1/(x+1998)-1/(x+1999)]
=1/x-1/(x+1999)
=1998/x(x+1999)
x(x+1999)分之1998
1/x-1/(x+1)+1/(x+1)-1/(x+2)+....+1/(x+1998)-1/(x+1999)
=1/x-1/(x+1999)
=1999/x(x+1999)
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