①计算[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].②利用上题的思路计算:{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 10:30:19
①计算[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].②利用上题的思路计算:{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a

①计算[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].②利用上题的思路计算:{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+
①计算[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].
②利用上题的思路计算:{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+2009)]}+{1/[(a+2009)(a+2010)]}的值.

①计算[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].②利用上题的思路计算:{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+
[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].
=1-1/2+1/2-1/3+1/3-1/4+……+1/10+1/11
=1-1/11
=10/11
{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+2009)]}+{1/[(a+2009)(a+2010)]}
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+……+1/(a+2009)-1/(a+2010)
=1/a-1/(a+2010)
=2010/[a(a+2010)]

①10/11
②1/a-1/(a+2010)

[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/10-1/11)
=1-1/11=10/11
{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+2009)]}+{1/[(a+20...

全部展开

[1/(1×2)]+[1/(2×3)]+[1/(3×4)]+……+[1/(10×11)].
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/10-1/11)
=1-1/11=10/11
{1/[a(a+1)]}+{1/[(a+1)(a+2)]}+{1/[(a+2)(a+3)]}+……+{1/[(a+2008)(a+2009)]}+{1/[(a+2009)(a+2010)]}
=1/a-1/(a+2010)

收起

1/a(a+1)=1/a-1/(a+1)