有一串数列为：1,2,3,5,8,13,21,34,55,89......,求数列{An}的通项公式。_百度知道
有一串数列为：1,2,3,5,8,13,21,34,55,89......,求数列{An}的通项公式。
2　　则F(n)=C1*X1^n + C2*X2^n　　∵F(1)=F(2)=1　　∴C1*X1 + C2*X2　　C1*X1^2 + C2*X2^2　　解得C1=1&#47，r=(1-√5)/=3)，F(1)=F(2)=1　　上式可化简得;√5;&#47,β=(1+√5)&#47斐波那契数列;2]^(n-2)*(a2-(1-√5)&#47， -rs=1　　n≥3时、以r^(n-1)为末项;2或α=(1+√5)&#47,an=a(n-1)+a(n-2)(n&2*(a(n-1)-(1+√5)&#47,化简得an=(1/SPAN&s]&#47，有　　F(n)-r*F(n-1)=s*[F(n-1)-r*F(n-2)]　　F(n-1)-r*F(n-2)=s*[F(n-2)-r*F(n-3)]　　F(n-2)-r*F(n-3)=s*[F(n-3)-r*F(n-4)]　　……　　F(3)-r*F(2)=s*[F(2)-r*F(1)]　　将以上n-2个式子相乘;√5)*{[(1+√5)/2]^(n-2)*(a2-(1-√5)/√5)*{[(1+√5)&#47，得、……　　如果设F(n)为该数列的第n项(n∈N+);/&2;2]^n}　　`````&lt,β=(1-√5)/2*a1)`````````1　　an-(1+√5)&#47，F(1)=F(2)=1：　　F(n)=s^(n-1)+r*F(n-1)　　= s^(n-1) + r*s^(n-2) + r^2*F(n-2)　　= s^(n-1) + r*s^(n-2) + r^2*s^(n-3) + r^3*F(n-3)　　……　　= s^(n-1) + r*s^(n-2) + r^2*s^(n-3) +……+ r^(n-2)*s + r^(n-1)*F(1)　　= s^(n-1) + r*s^(n-2) + r^2*s^(n-3) +……+ r^(n-2)*s + r^(n-1)　　（这是一个以s^(n-1)为首项：1;p&gt,解得α=(1-√5)&#47。那么这句话可以写成如下形式;√5　　∴F(n)=(1/s)　　=(s^n - r^n)/(s-r)　　r+s=1;-x-1=0,可得　　an=[(1+√5)&#47、1、r/2]^n}（√5表示根号5）　　通项公式的推导方法二;2]^(n-2)*(a2-(1+√5)/2]^n}　　迭代法　　已知a1=1,a2=1;√5)*{[(1+√5)/2]^n - [(1-√5)&#47。　　通项公式的推导方法一;2　　则F(n)=(1&#47、5;2　　所以　　an-(1-√5)/2;(1-r/2;2*a(n-2))=[(1+√5)&#47：　　F(n)-r*F(n-1)=[s^(n-2)]*[F(2)-r*F(1)]　　∵s=1-r;2*a(n-2))=[(1-√5)/&#47、2;2]^n - [(1-√5)&#47，C2=-1&#47、3，X2=(1-√5)/2;SPAN&2*a(n-1)=(1+√5)/2]^(n-2)*(a2-(1+√5)/2]^n - [(1-√5)&#47、21;2*a1)``````````````3　　an=[(1-√5)&#47、8,式2,;2-式4*(1-√5)&#47:设an-αa(n-1)=β(a(n-1)-αa(n-2))　　得α+β=1　　αβ=-1　　构造方程x²2：　　F(0) = 0，s　　使得F(n)-r*F(n-1)=s*[F(n-1)-r*F(n-2)]　　则r+s=1：　　X^2=X+1　　解得　　X1=(1+√5)/2*a1)`````````2　　由式1;s为公比的等比数列的各项的和）　　=[s^(n-1)-r^(n-1)*r/2*(a(n-1)-(1-√5)&#47， -rs=1的一解为 s=(1+√5)&#47：利用特征方程　　线性递推数列的特征方程为，F(n)=F(n-1)+F(n-2) (n≥3)　　显然这是一个线性递推数列,求数列{an}的通项公式　　解 ;&lt、13：普通方法　　设常数r;2*a(n-1)=(1-√5)/2*a1)``````````````4　　将式3*(1+√5)&#47：　　F(n)=s^(n-1)+r*F(n-1)　　那么
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An+2=An+1+An
An=A(n-1)+A(n-2)
f(n)=f(n-2)
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Time: <font color="#15-07-17 22:35:39 (CST)
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7.11.248.156
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AVL SDK 3.0
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9.0.0.4157
9.0.0.4157
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4.1.3.52192
bitdefender
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5.0.2.3300
26.749, 26.749
6.5.1.5418
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V1.32.31.0
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9.500-1005
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25.17.00.04
25.17.00.04
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3.9.2589.2
3.9.2589.2
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17.47.17308
1.0.2.2108
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virusbuster
15.0.985.0
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解得α=2028/8β=A28289^^^9=A9=9/28
解得α=2028/8β=A28289^^^9=A9=9/28
b28 c28-28ab-28bc 28ca-c a28/28c28}