caculation:2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + .+ (2+3+4+...+2009)/(1+2+3+4+...+2009)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 20:11:39
caculation:2/(1+2)+(2+3)/(1+2+3)+(2+3+4)/(1+2+3+4)+.+(2+3+4+...+2009)/(1+2+3+4+...+2009)caculation:2

caculation:2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + .+ (2+3+4+...+2009)/(1+2+3+4+...+2009)
caculation:
2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + .+ (2+3+4+...+2009)/(1+2+3+4+...+2009)

caculation:2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + .+ (2+3+4+...+2009)/(1+2+3+4+...+2009)
1-1/(1+2)+1-1/(1+2+3)+1-1/(1+2+3+4)+……+1-1/(1+2+3+4+...+2009)
=2008-【1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+……+1/(1+2+3+4+...+2009)】
=2008-2×【(1/6+1/12+1/24+……+1/(2009×2010)】
=2008-2×(1/2-1/2010)
=2007+1/1005

2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + ....+ (2+3+4+...+2009)/(1+2+3+4+...+2009)
=2008-[1/(1+2) + 1/(1+2+3) +1/(1+2+3+4) + ....+ 1/(1+2+3+4+...+2009)]
=2008-(2/2*3+2/3*4+2/4*5+……+2/2009*...

全部展开

2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + ....+ (2+3+4+...+2009)/(1+2+3+4+...+2009)
=2008-[1/(1+2) + 1/(1+2+3) +1/(1+2+3+4) + ....+ 1/(1+2+3+4+...+2009)]
=2008-(2/2*3+2/3*4+2/4*5+……+2/2009*2010)
=2008-2*(1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/2010)
=2008-2*(1/2-1/2010)
=2008-(1-1/1005)
=2007又1/1005

收起

通项公式为:(n(n+1)-2)/(n(n+1))=1-2/(n(n+1))=1-2(1/n-1/(n+1))
所以原式=
1x2008 - 2x(1/2 - 1/3 + 1/3 -1/4 +。。。+1/2009 -1/2010)
=2008-2x(1/2-1/2010)
=2008-1+1/1005
=2007又1/1005

会不会:(2+3+...+n)/(1+2+3+...+n)=[(n+2)(n-1)/2]/[(n+1)n/2]=1-2/[n(n+1)]=1-2[1/n-1/(n+1)]

2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + ....+ (2+3+4+...+2009)/(1+2+3+4+...+2009)
=1-2(1/2-1/3)...

全部展开

会不会:(2+3+...+n)/(1+2+3+...+n)=[(n+2)(n-1)/2]/[(n+1)n/2]=1-2/[n(n+1)]=1-2[1/n-1/(n+1)]

2/(1+2) + (2+3)/(1+2+3) +(2+3+4)/(1+2+3+4) + ....+ (2+3+4+...+2009)/(1+2+3+4+...+2009)
=1-2(1/2-1/3)+1-2(1/3-1/4)+1-2(1/4-1/5)+...+1-2(1/2009-1/2010)
=2009-1-2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010)
=2008-2(1/2-1/2010)
=2008-1+1/1005
=2007又1/1005

收起