作业帮n(n+2)分之+(n+2)(n+4)分之1+(n+4)(n+6)分之1+(n+6)(n+8)分之1+···(n+2006)(n+教教我!
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/27 17:27:09
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n(n+2)分之+(n+2)(n+4)分之1+(n+4)(n+6)分之1+(n+6)(n+8)分之1+···(n+2006)(n+教教我!
n(n+2)分之+(n+2)(n+4)分之1+(n+4)(n+6)分之1+(n+6)(n+8)分之1+···(n+2006)(n+
教教我!
n(n+2)分之+(n+2)(n+4)分之1+(n+4)(n+6)分之1+(n+6)(n+8)分之1+···(n+2006)(n+教教我!
1/n(n+2)=1/2[1/n-1/(n+2)];
1/(n+2)(n+4)=1/2[1/(n+2)-1/(n+4)];
1/(n+4)(n+6)=1/2[1/(n+4)-1/(n+6)];
...
1/(n+2006)(n+2008)=1/2[1/(n+2006)-1/(n+2008)];
1/n(n+2)+1/(n+2)(n+4)+1/(n+4)(n+6)+...+1/(n+2006)(n+2008)
=1/2[1/n-1/(n+2)+1/(n+2)-1/(n+4)+1/(n+4)-1/(n+6)+.+1/(n+2006)-1/(n+2008);
=1/2[1/n-1/(n+2008)]
=1/2[2008/n(n+2008)]
=1004/[n(n+2008)]
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