1/1x2+1/(1+1)(2+1)+1/(1+2）x（2+2)+1/(1+3)x(2+3)+...+1/(1+2009)x(2+_数学解答

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

人气：270 ℃　时间：2020-06-30 12:28:52

解答

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