1/1x2+1/(1+1)(2+1)+1/(1+2)x(2+2)+1/(1+3)x(2+3)+...+1/(1+2009)x(2+2009)的值

问题描述:

1/1x2+1/(1+1)(2+1)+1/(1+2)x(2+2)+1/(1+3)x(2+3)+...+1/(1+2009)x(2+2009)的值

用拆项法做
1/1x2=1-1/2
1/(1+1)(2+1)=1/2-1/3
1/(1+2)x(2+2)=1/3-1/4
.
1/(1+2009)x(2+2009)=1/2010-1/2011
累加得出结果1-1/2011=2010/2011