1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008
来源:百度知道 编辑:UC知道 时间:2024/05/18 07:34:47
已知:1/1*2=1-1/2 1/2*3=1/2-1/3
则1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008==?
则1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008==?
用裂项级数的方法做:
1/1*2+1/2*3+1/3*4+...+1/2006*2007+1/2007*2008
=[1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008]
中间的都抵消,首尾各剩下一项
=1-1/2008
=2007/2008
=1-1/2+1/2-1/3+1/3...-1/2007+1/2007-1/2008
=1-1/2008
=2007/2008
1-1/2+1/2-1/3+..-1/2008=2007/2008
原式=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2006-1/2007)+(1/2007-1/2008)=1-1/2008=2007/2008
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
1+1/2+1/3+.....+1/n
1+1/2+1/3+...+1/100
1-1/2+1/3-.....-1/10
(1+1/2+1/3+1/4)×
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100)
1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100)
1+1/1+2+1/1+2+3+...+1/1+2+3...+2000
1+1/1+2+1/1+2+3.........+1/1+2+3.....100