计算2005/6+2005/12+2005/20+2005/30+...+2005/(2003×2004)+1/2004

2005/2-2005/3
+ 2005/3-2005/4
+
.
.
.
.
+2005/2003-2005/2004
+1/2004
=2005/2-2005/2004+1/2004
=2005/2-1
=2003/2

原式=2005×(1/2×3+1/3×4+1/4×5+1/5×6+...+1/2003×2004)+1/2004
=2005×(1/2-1/3+1/3-1/4+1/4-1/5+1/5+1/6+...+1/2003-1/2004)+1/2004
=2005×(1/2-1/2004)+1/2004
=2005/2-2005/2004+1/2004
=2005/2-1
=2003/2

2005/6+2005/12+2005/20+2005/30+...+2005/(2003×2004)+1/2004
=2005×【1/6+1/12+1/20+1/30+……+1/（2003×2004）】+1/2004
=2005×（1/2-1/3+1/3-1/4+1/4-1/5+……+1/2003-1/2004）+1/2004
=2005×（1/2-1/2004）+1/2004
=2005×1001/2004+1/2004
=2005000/2004+2005/2004+1/2004
=2007006/2004
=1001.5

你是不是输入有问题啊？

原式=2005*(1/(2*3)+1/(3*4)+...+1/(2003*2004))+1/2004
=2005*(1/2-1/3+1/3-1/4+...+1/2003-1/2004)+1/2004
=2005*(1/2-1/2004)+1/2004
=2005/2-1
=2003/2

用excel在任何单元格中输入 = 及你要计算的内容，回车。