计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2008)(x+2009)

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/14 03:14:53

计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2008)(x+2009)
计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2008)(x+2009)

计算:1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2008)(x+2009)
1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+2008)(x+2009)
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+.+1/(x+2008)-1/(x+2009)
=1/x-1/(x+2009)
=[(x+2009)-x] / [x(x+2009)]
=2009 / [x(x+2009)]