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
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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1/1x2+1/(1+1)(2+1)+1/(1+2）x（
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
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
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
/(n+1)(n+2)=1/(n+1)-1/(n+2)
因此
原式=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/1996-1/1997)
=1-1/1997
=1996/1997
2011
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