已知数列{a}满足a1=2,an-1=2an+1/2,求a2011的值,

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已知数列{a}满足a1=2,an-1=2an+1/2,求a2011的值,已知数列{a}满足a1=2,an-1=2an+1/2,求a2011的值,已知数列{a}满足a1=2,an-1=2an+1/2,求

已知数列{a}满足a1=2,an-1=2an+1/2,求a2011的值,
已知数列{a}满足a1=2,an-1=2an+1/2,求a2011的值,

已知数列{a}满足a1=2,an-1=2an+1/2,求a2011的值,
an-1=2an+1/2
2an+1/2+1/2=2(an+1/2)=a(n-1)+1/2
(an+1/2)/[a(n-1)+1/2]=1/2
令bn=an+1/2,b1=a1+1/2=5/2
数列{bn}是一个首项是5/2,公比是1/2的等差数列
bn=5/2*(1/2)^(n-1)=5*(1/2)^n
an=bn-1/2=5*(1/2)^n-1/2
a2011=5*(1/2)^2011-1/2

a(n-1)+1/2=2(an+1/2)
(an+1/2)/[a(n-1)+1/2]=1/2
a1+1/2=2+1/2=5/2
可知，{an+1/2}是以5/2为首项，1/2为公比的等比数列
则有：an+1/2=(5/2)*(1/2)^(n-1)
则，an=(5/2)*(1/2)^(n-1)-1/2
则，a2011=(5/2)*(1/2)^2010-1/2

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