解方程1/(x+)(x+2)+1/(x+2)(x+3)+...1/(x+99)(x+100)+1/x+100=2009/2010 帮帮忙,明天就交了,谢谢了~

x=2009

1/(x+1)(x+2)+1/(x+2)(x+3)+...1/(x+99)(x+100)+1/x+100
=(1/(x+1)-1/(x+2))+(1/(x+2)-1/(x+3))+...+(1/(x+99)-1/(x+100))+1/x+100)
=1/(x+1)=2009/2010
x=2009

1/(x+1)(x+2) 这个等于1/(x+1)-1/(x+2)
依次类推.
1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+99)-1/(x+100)+1/(x+100)=2009/2010;
所以1/(x+1)=2009/2010;
解得x=1/2009