mathematica 数列1）已知数列x[1]=2,x[n]=(2+(x[n-1])^1/2)^1/2,画数列散点图,列表前30项并求极限2）已知C[n]的递推关系为 C[0]=C[1]=C[2]=1,n>=2时 C[N+1]=C[N-1]+C[N-2] ,列表前50项

mathematica 数列1）已知数列x[1]=2,x[n]=(2+(x[n-1])^1/2)^1/2,画数列散点图,列表前30项并求极限2）已知C[n]的递推关系为 C[0]=C[1]=C[2]=1,n>=2时 C[N+1]=C[N-1]+C[N-2] ,列表前50项
mathematica 数列
1）已知数列x[1]=2,x[n]=(2+(x[n-1])^1/2)^1/2,画数列散点图,列表前30项并求极限
2）已知C[n]的递推关系为 C[0]=C[1]=C[2]=1,n>=2时 C[N+1]=C[N-1]+C[N-2] ,列表前50项

mathematica 数列1）已知数列x[1]=2,x[n]=(2+(x[n-1])^1/2)^1/2,画数列散点图,列表前30项并求极限2）已知C[n]的递推关系为 C[0]=C[1]=C[2]=1,n>=2时 C[N+1]=C[N-1]+C[N-2] ,列表前50项
1)我的做法：
x[n_] := (2 + x[n - 1]^(1/2))^(1/2);
x[1] = 2;
TableForm[Array[x,30],TableHeadings -> Automatic]
ListPlot[Array[x,30],AxesOrigin -> {0,0},
PlotStyle -> PointSize[0.01],PlotRange -> {-1,3}]
Solve[a == (2 + a^(1/2))^(1/2),a](*设极限为a,则有*)
2）
c[n_] := c[n - 2] + c[n - 3];
c[0] = c[1] = c[2] = 1;
Prepend[Array[c,49],c[0]]
你粘贴 复制 运行一下看看 结果图片我就不传了

1可以用matlab计算程序

x(1)=2;

for i=2:30

    x(i)=(2+x(i-1)^0.5)^0.5;

end

x

for i=1:30;

    y(1,i)=i;

end<...

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1可以用matlab计算程序

x(1)=2;

for i=2:30

    x(i)=(2+x(i-1)^0.5)^0.5;

end

x

for i=1:30;

    y(1,i)=i;

end

y(1,:)

plot(y(1,:),x ,'r.',y(1,:),x);

极限是1.8312

前三十个数是

  Columns 1 through 12

    2.0000    1.8478    1.8328    1.8313    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312

  Columns 13 through 24

    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312

  Columns 25 through 30

    1.8312    1.8312    1.8312    1.8312    1.8312    1.8312

2  x(1)=1;

x(2)=1;

x(3)=1;

 for i=3:50

    x(i+1)=x(i-1)+x(i-2);

 end

x

x =

           1           1           1           2           2           3           4           5           7           9

          12          16          21          28          37          49          65          86         114         151

         200         265         351         465         616         816        1081        1432        1897        2513

        3329        4410        5842        7739       10252       13581       17991       23833       31572       41824

       55405       73396       97229      128801      170625      226030      299426      396655      525456      696081

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