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1、实验二：极限与连续第一题：数列极限In[1]=f[n_]:=Sum[1/j^3,{j,1,n}];xn=Table[N[f[n],10],{n,30}]Out[1]={1.000000000,1.125000000,1.162037037,1.177662037,1.185662037,1.190291667,1.193207119,1.195160244,1.196531986,1.197531986,1.198283300,1.198862004,1.199317170,1.199681602,1.199977898,1.200222
2、039,1.200425580,1.200597048,1.200742842,1.200867842,1.200975822,1.201069736,1.201151926,1.201224264,1.201288264,1.201345159,1.201395965,1.201441518,1.201482521,1.201519558}In[2]=ListPlot[xn,PlotStyle®PointSize[0.02]]Out[2]=Graphics第二题：递归数列In[3]=Clear[f];f[1]=1;f[n_]:=f[n]
3、=N[(f[n-1]+3/f[n-1])/2,20];fn=Table[f[n],{n,30}]Out[3]={1,2.0000000000000000000,1.7500000000000000000,1.7321428571428571429,1.7320508100147275405,1.7320508075688772953,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.73205080756887
4、72935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.
5、7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935,1.7320508075688772935}In[4]=ListPlot[fn,PlotStyle®PointSize[0.02]]Out[4]=Graphics第三题：多次自复合In[5]=Plot[{Sin[x],Nest[Sin,x,5],Nest[Sin,x,10],Nest
6、[Sin,x,30]},{x,-2Pi,2Pi},PlotStyle®{RGBColor[0,0,1],RGBColor[1,1,0],RGBColor[1,0,0],RGBColor[0,1,0]}]Out[5]=GraphicsIn[6]=Clear[f];f[n_]:=f[n]=Nest[Sin,3,n];fn=Table[N[f[n],10],{n,30}]Out[6]={0.1411200081,0.1406520768,0.1401887818,0.1397300469,0.1392757977,0.1388259614,0.
7、1383804669,0.1379392448,0.1375022270,0.1370693472,0.1366405402,0.1362157427,0.1357948923,0.1353779282,0.1349647910,0.1345554222,0.1341497650,0.1337477635,0.1333493630,0.1329545100,0.1325631521,0.1321752379,0.1317907173,0.1314095408,0.1310316604,0.1306570285,0.1302855991,0
8、.1299173265,0.1295521663,0.1291900748}In[7]=ListPlot[fn,PlotStyle®PointSize[0.02]]Out[7]=Graphic
