解方程1/(x+)(x+2)+1/(x+2)(x+3)+…1/(x+99)(x+100)+1/x+100=2009/2010 幫幫忙,明天就交了,謝謝了~

解方程1/(x+)(x+2)+1/(x+2)(x+3)+…1/(x+99)(x+100)+1/x+100=2009/2010 幫幫忙,明天就交了,謝謝了~

1/(x+1)(x+2)這個等於1/(x+1)-1/(x+2)
依次類推.
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