1x2+2x3+3x4+.+2011x2012

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 22:25:58
1x2+2x3+3x4+.+2011x2012

1x2+2x3+3x4+.+2011x2012
1x2+2x3+3x4+.+2011x2012

 

1x2+2x3+3x4+.+2011x2012
整数裂项
1/(2011×2012)×(1×2+2×3+...+2011×2012)
=1/(2011×2012)×(2011×2012×2013)/3
=2013/3
=671

1x2+2x3+3x4+。。。+2011x2012
= 2011x2012x2013 / 3

所以 最后算式 = 2013/3 = 671

2011*2012*2013/3

由题意
1x2+2x3+3x4+。。。+2011x2012
=2010x(2011x2012) / 3+3x(2011x2012)/3
=2011x2012x2013/3

所以上面结果就是
(1/2011x2012) x 2011x2012x2013/3
=2013/3

=671

671

=1/(2011*2012)*2011*2012*2013/3
=2013/3=671

因为1x2+2x3+3x4+。。。+2011x2012 共有2011项,
所以
1x2+2x3+3x4+。。。+2011x2012=2011X2012X2013/3
[1/(2011X2012)]X1x2+2x3+3x4+。。。+2011x2012
=[1/(2011X2012)]X2011X2012X2013/3
=2013/3=671

根据上面列出的规律,可以得出:

(1x2+2x3+3x4+…+2011x2012)=(2011x2012x2013)/3

所以:

1/(2011x2012)x(1x2+2x3+3x4+…+2011x2012)=2013/3 

 

 

 

 

 

(1*2+2*3+3*4.....+2011*2012)/(2011*2012)

=2011*2012*2013/3/(2011*2012)=2013/3=671