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+
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![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+](/uploads/image/z/759931-43-1.jpg?t=%E2%91%A0%E8%AE%A1%E7%AE%97%5B1%EF%BC%8F%EF%BC%881%C3%972%EF%BC%89%5D%EF%BC%8B%5B1%EF%BC%8F%EF%BC%882%C3%973%EF%BC%89%5D%EF%BC%8B%5B1%EF%BC%8F%EF%BC%883%C3%974%EF%BC%89%5D%EF%BC%8B%E2%80%A6%E2%80%A6%EF%BC%8B%5B1%EF%BC%8F%EF%BC%8810%C3%9711%EF%BC%89%5D.%E2%91%A1%E5%88%A9%E7%94%A8%E4%B8%8A%E9%A2%98%E7%9A%84%E6%80%9D%E8%B7%AF%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BD%9B1%EF%BC%8F%5Ba%EF%BC%88a%2B1%EF%BC%89%5D%EF%BD%9D%EF%BC%8B%EF%BD%9B1%EF%BC%8F%5B%EF%BC%88a%2B1%EF%BC%89%EF%BC%88a%2B2%EF%BC%89%5D%EF%BD%9D%EF%BC%8B%EF%BD%9B1%EF%BC%8F%5B%EF%BC%88a%2B2%EF%BC%89%EF%BC%88a%2B3%EF%BC%89%5D%EF%BD%9D%EF%BC%8B%E2%80%A6%E2%80%A6%2B%EF%BD%9B1%EF%BC%8F%5B%EF%BC%88a%2B2008%EF%BC%89%EF%BC%88a%2B)
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...
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[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)
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1/a(a+1)=1/a-1/(a+1)