Question

初一数学题，求助

观察下列各式
1/2=1/1*2=1/1-1/2，1/6=1/2*3=1/2-1/3……
1、用n表示等式
2、利用得出的结论，计算1/x（x+1）+1/（x+1）（x+2）+……+1/（x+4）（x+5）
第二题：已知1/x-1/y=3，求5x+xy-5y/x-xy-y

Answer 1

1.
1/[n*(n+1)]=1/n-1/(n+1)
2.
1/x（x+1）+1/（x+1）（x+2）+……+1/（x+4）（x+5）
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
=[(x+5)-x]/(x*(x+5)
=5/(x^2+5x)

已知1/x-1/y=3，求5x+xy-5y/x-xy-y
1/x-1/y=3
(y-x)/xy=3
y-x=3xy

(5x+xy-5y)/(x-xy-y)
=[5(x-y)+xy]/[(x-y)-xy]
=[5*(-3xy)+xy]/[-3xy-xy]
=-14xy/(-4xy)
=7/2

Answer 2

1/n*(n+1)=1/n-1/(n+1)

1/x-1/(x+5)

Answer 3

1/(n*(n+1))=1/n-1/(n+1)
1/x（x+1）+1/（x+1）（x+2）+……+1/（x+4）（x+5）
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+……+1/(x+4)-1/(x+5)
=1/x-1/(x+5)
5/(x*(x+5))

1/x-1/y=3，求5x+xy-5y/x-xy-y (应该是(5x+xy-5y)/(x-xy-y))吧）
1/x-1/y=3
y-x=3xy
(5x+xy-5y)/(x-xy-y)
=[5(x-y)+xy]/[(x-y)-xy]
=[5*(-3xy)+xy]/[-3xy-xy]
=-14xy/(-4xy)
=7/2

Answer 4

1. 1/n(n+1)=1/n-1/n+1
2.原式=1/x - 1/x+1 + 1/x+1 - 1/x+2 + 1/x+2 …… - 1/x+5
=1/x - 1/x+5

二：原式通分得：y-x/xy =3 所以y-x=3xy 所以原式= 5（x-y）+xy/(x-y)-xy =-15xy+xy/-5xy-xy =7/3