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x²-3x 1=0 1/1x2+1/2x3+1/3x4+1/4x5+.+1/2008x2009 =?(用简便计算)数学问题请大家帮忙做下

火烧 2022-12-14 08:56:59 1078
1/1x2+1/2x3+1/3x4+1/4x5+.+1/2008x2009 =? 用简便计算)数学问题请大家帮忙做下 1/1x2+1/2x3+1/3x4+1/4x5+...+1/2008x2009 =

1/1x2+1/2x3+1/3x4+1/4x5+.+1/2008x2009 =?(用简便计算)数学问题请大家帮忙做下  

1/1x2+1/2x3+1/3x4+1/4x5+...+1/2008x2009 =?(用简便计算)数学问题请大家帮忙做下

1/1x2+1/2x3+1/3x4+1/4x5+...+1/2008x2009 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2008-1/2009 =1-1/2009 =2008/2009

1/1x2+1/2x3+1/3x4+1/4x5...1/2001x2002 简便计算

1/1x2+1/2x3+1/3x4+1/4x5...1/2001x2002
=1-1/2+1/2-1/3+1/3-1/4+....+1/2001-1/2002
=1-1/2002
=2001/2002

1/1x2+1/2x3+1/3x4+1/4x5+...+1/2009x2010

1/1x2+1/2x3+1/3x4+1/4x5+...+1/2009x2010
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010
=1-1/2010
=2009/2010

1/1X2+1/2X3+1/3X4+...+1/2008X2009

通式
1/N(N+1)+1/(N+1)(N+2)......=1/1-1/2+1/2-1/3.....+1/2008-1/2009
中间约掉
1-1/2009=2008/2009

1/1X2+1/2X3+1/3X4+1/4X5+...+1/2010X2011

做了将近半个小时没做出来,突然想出来了,该题好像在课本上有,觉得太简单了。
将题目化为:1/nx(n+1)=1/n---1/(n+1)带入式子得:中间的全消掉了,
最后剩下的是1-1/2011=2010/2011!

x²-3x 1=0 1/1x2+1/2x3+1/3x4+1/4x5+.+1/2008x2009 =?(用简便计算)数学问题请大家帮忙做下

数学题。急求高手解答1/1x2+1/2x3+1/3x4+1/4x5+.....+1/2007x2008+1/2008x2009帮忙列出每个步骤,谢谢

1/1x2+1/2x3+1/3x4+1/4x5+.....+1/2007x2008+1/2008x2009
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2008-1/2009)
=1-1/2009
=2008/2009
学了数列 裂项 后 就会做了

1/2X3+1/3X4+1/4X5+~~~~~1/2008X2009找规律,算结果

一休08252,你好:

1/2×3+1/3×4+1/4×5+......+1/2008×2009
=1/2-1/3+1/3-1/4+1/4-1/5+......+1/2008-1/2009
=1/2-1/2009
=2009/4018-2/4018
=2007/4018

数学智力乐园规律 1/1x2+1/2x3= 1/1x2+1/2x3+1/3x4= 1/1x2+1/2x3+1/3x4+1/4x5= 要规律

1/1x2=1/1-1/2;
1/2x3=1/2-1/3;
1/3x4=1/3-1/4;
1/4x5=1/4-1/5;
……
所以:
1/1x2+1/2x3=1/1-1/2+1/2-1/3=1-1/3=2/3;
1/1x2+1/2x3+1/3x4=1/1-1/2+1/2-1/3+1/3-1/4=1-1/4=3/4;
1/1x2+1/2x3+1/3x4+1/4x5=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5=1-1/5=4/5;
……

七年级数学题 1/1x2+1/2x3+1/3x4+1/4x5+......+1/2007x2008=多少 怎么计算

1/1x2+1/2x3+1/3x4+1/4x5+......+1/2007x2008(任何一项积分母分之一可化成两个互减单项式形式,没什么公式,只是个特例)
=(1/1-1/2)+ (1/2-1/3)+(1/3-1/4)+(1/4-1/5)+,,,,,,+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/2007-1/2008
=1-1/2008(中间项全部抵消,只剩下两端的项)
=2007/2008

简便计算1/2+1/2x3+1/3x4+1/4x5+...+1/99x100

原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100
=1-1/100
=99/100

明白请采纳,有疑问请追问!
有新问题请求助,谢谢!

  
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