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已知Sn为数列{an}的前项和,且Sn=2an+n2-3n-2,n=1,2,3…
(Ⅰ)求证:数列{an-2n}为等比数列;
(Ⅱ)设bn=an•(-1)n,求数{bn}的n项和Pn;
(Ⅲ)设cn=,数列{cn}的n项和为Tn,求证:Tn<.
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已知Sn为数列{an}的前n项和,且Sn=2an+n2-3n-2,n=1,2,3….
(Ⅰ)求证:数列{an-2n}为等比数列;
(Ⅱ)设bn=an•cosnπ,求数列{bn}的前n项和Pn;
(Ⅲ)设,数列{cn}的前n项和为Tn,求证:.
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已知Sn为数列{an}的前n项和,且Sn=2an+n2-3n-2(n=1,2,3…).令bn=an-2n(n=1,2,3…).
(Ⅰ)求证:数列{bn}为等比数列;
(Ⅱ)令,记Tn=c1c2+2c2c3+22c3c4+…+2n-1cncn+1,比较Tn与的大小.
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在等比数列{an}中,a1=2,前n项和为sn,若数列{an+1}也是等比数列,则sn等于( )
A.2n+1-2
B.3n2
C.2n
D.3n-1
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数列{an}的前n项和为Sn,若对于任意的正整数n都有Sn=2an﹣3n.
(1)设bn=an+3,求证:数列{bn}是等比数列,并求出{an}的通项公式;
(2)求数列{nan}的前n项和.
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数列{an}的前n项和为Sn,若对于任意的正整数n都有Sn=2an-3n.
(1)设bn=an+3,求证:数列{bn}是等比数列,并求出{an}的通项公式;
(2)求数列{nan}的前n项和.
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数列{an}的首项为a1,通项为an,前n项和为Sn,则下列说法中:
①若Sn=n2+n,则{an}为等差数列;
②若Sn=2n-1,则{an}为等比数列;
③若2an=an+1+an-1(n≥2),则{an}为等差数列;
④若an2=an+1•an-1(n≥2),则{an}为等比数列;
正确的序号是________.
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已知数列{f(n)}的前n项和为Sn,且Sn=n2+2n.
(1)求数列{f(n)}通项公式;
(2)若a1=f(1),an+1=f(an)(n∈N*),求证数列{an+1}是等比数列,并求数列{an}的前n项和Tn.
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已知数列{an}的前n项和为Sn,且满足Sn+n=2an(n∈N*).
(1)证明:数列{an+1}为等比数列,并求数列{an}的通项公式;
(2)若bn=an+2n+1,数列{bn}的前n项和为Tn..
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已知数列中, a2=7,且an =an+1-6(n∈),则前n项和Sn=" (" )
A. B. n2 C. D.3n2 –2n