求一道数学题：x/(1*2)+x/(2*3).+x/(2008*2009）=2008
问题描述：
求一道数学题：x/(1*2)+x/(2*3).+x/(2008*2009）=2008
答
(1-1/2)x+(1/2-1/3)x+……+(1/2008-1/2009)x=2008
（1-1/2+1/2-1/3+……+1/2008-1/2009)x=2008
(1-1/2009)x=2008
2008x/2009=2008
x=2009
答
1/(n*(n+1))=1/n-1/(n+1)
提出x
1/(1*2)+1/(2*3)......+1/(2008*2009）
=1/1-1/2+1/2-1/3+...+1/2008-1/2009
=1-1/2009
=2008/2009
x=2009
答
x(1/1*2+1/2*3+……+1/2008*2009)=2008
x[(1-1/2)+(1/2-1/3)+……+(1/2008-1/2009)]=2008
x(1-1/2009)=2008
x(2008/2009)=2008
x=2008÷(2008/2009)
x=2009