数学题在线解答1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)（x+4)+.+1/(x+99)(x+100)当x=5时，求代数式的值。

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数学题在线解答1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)当x=5时，求代数式的值。
数学题在线解答1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)
当x=5时，求代数式的值。

数学题在线解答1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)当x=5时，求代数式的值。
1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+.+1/(x+99)*(x+100)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)
=1/(x+1)-1/(x+100)
=99/ (x+1)(x+100)
x=5时
原式=99/(6*105)
=11/70

1/(X+1)-1/(X+100)

1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+......+1/(x+99)*(x+100)
=1/（x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)……+1/（x+99)-1/(x+100)
=1/(x+1)-1/(x+100)
=99/(x+1)(x+100)

1/(x+1)*(x+2)+1/(x+2)*(x+3)+1/(x+3)*（x+4)+......+1/(x+99)*(x+100)
=1/（x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)……+1/（x+99)-1/(x+100)
=1/(X+1)-1/(X+100) =1/6-1/105=11/70

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