计算(x+1)(x+2)/1+(x+2)(x+3)/1+(x+3)(x+4)/1+……+(x+2008)(x+2009)/1RT

分类: 作业答案 • 2021-12-18 16:25:29

问题描述：

计算(x+1)(x+2)/1+(x+2)(x+3)/1+(x+3)(x+4)/1+……+(x+2008)(x+2009)/1
RT

答

=1/（x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+……+1/(x+2008)-1/(x+2009)
=1/(x+1)-1/(x+2009)
=2008/(x+1)(x+2009)
你的除号写反了吧...

答

拆项法,应用公式1/[n(n+1)]=1/n-1/(n+1):
原式=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+2008)-1/(x+2009)
=1/(x+1)-1/(x+2009)
=2008/[(x+1)(x+2009)]