2005/1×2+2005/3×4+.......+2005/2004×2005=?
来源:百度知道 编辑:UC知道 时间:2024/06/05 02:39:11
2005/1×2+2005/2*3+.......+2005/2004×2005
=2005*[1/1*2+1/2*3+..+1/2004*2005]
=2005[1-1/2+1/2-1/3+...+1/2004-1/2005]
=2005[1-1/2005]
=2005*2004/2005
=2004
因为1/n×(n+1)=1/n-1/n+1
所以原式=2005×(1/1×2+1/3×4+……+1/2004×2005)
=2005×(1/1-1/2+1/3-1/4+……+1/2004-1/2005)
题目是不是打错了?
1/2+6/1+1/15+1/20……1/2005*2006
(1-1/2005)+(1-2/2005)+(1-3/2005)+..............(1-2003/2005))+(1-2004/2005)
1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=?
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
1/2+1/(2*3)+1/(3*4)+......+1/(2004*2005)+1/(2005*2006)
1+1/2+1/3+.....+1/2005][1/2+1/3+.......+1/2006]-[1/2+1/3+......+1/2005][1+1/2+1/3+1/2006]
计算(1/2+1/3+...+1/2005)(1+1/2+1/3+...+1/2004)-(1+1/2+1/2005)(1/2+1/3+...+1/2004)
1/(1*2)+1(2*3)+1/(3*4)+........+1/(2005*2006)
2005/1*2+2005/2*3+2005/3*4+2005/4*5+~~~+2005/2004*2005=?
1/1*3+1/2*4+1/3*5+......+1/2005*2007