(本小题满分14分)设函数f (x)满足f (0) =1,且对任意,都有f (xy+1) = f (x) f (y)-f (y)-x+2.(I)      求f

(本小题满分14分)设函数f (x)满足f (0) =1,且对任意,都有f (xy+1) = f (x) f (y)-f (y)-x+2.(I)      求f

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(本小题满分14分)设函数f (x)满足f (0) =1,且对任意,都有f (xy+1) = f (x) f (y)-f (y)-x+2.(I)      求f (x) 的解析式;(II)  若数列{an}满足:an+1=3f (an)-1(nÎ N*),且a1=1,求数列{an}的通项公式;
(Ⅲ)求数列{an}的前n项和Sn
答案
(Ⅰ)  (Ⅱ) an = 2×3n1-1(Ⅲ)3nn-2
解析
(I) ∵f (0) =1.
x=y=0得f (1) = f (0) f (0)-f (0)-0+2="2                                       "
再令y=0得,                              
所以                                                                          5分
(II) ∵,∴an+1=3f (an)-1= 3an+2,                                             
an+1+1=3(an+1),                                                                                 
a1+1=2,∴数列{an+1} 是公比为3的等比数列                            
an +1= 2×3n1,即an = 2×3n1-1                                                     10分
(III) Sn = a1 + a2 + … + an
=2×(30+31+32+ ×××××× + 3n1)-n
=3nn-2                                                                                           14分
举一反三
(本小题满分14分)
设数列的前项和为,对任意的正整数,都有成立,记
(Ⅰ)求数列的通项公式;
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(Ⅲ)设数列的前项和为。已知正实数满足:对任意正整数恒成立,求的最小值。
题型:不详难度:| 查看答案
(本小题满分12分)已知:数列与—3的等差中项。(1)求;(2)求数列的通项公式。
题型:不详难度:| 查看答案
(本小题满分12分)已知数列的各项为正数,前
(1)求证:数列是等差数列; (2)设
题型:不详难度:| 查看答案
若数列为等差数列,首项,公差,,则(      )
A.33B.34 C.35D.36

题型:不详难度:| 查看答案
已知等差数列的前项和为,若,,则它的首项与公差分别是(     )
A.B.C.D.以上都不对

题型:不详难度:| 查看答案
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