计算1/x(x+1)+1/(x+2)(x+1).+1/(x+2008)(x+2009)并求当x=1时,该代数式的值
问题描述:
计算1/x(x+1)+1/(x+2)(x+1).+1/(x+2008)(x+2009)并求当x=1时,该代数式的值
答
1/x(x+1)=1/x-1/(1+x)1/(x+2)(x+1)=1/(x+1)-1/(x+2).1/(x+2008)(x+2009)=1/(x+2008)-1/(1+2009)1/x(x+1)+1/(x+2)(x+1).+1/(x+2008)(x+2009)=1/x-1/(1+x)+1/(x+1)-1/(x+2)+.+1/(x+2008)-1/(x+2009)=1-1/(x+2009)...