数学实验二：极限与连续.docx

实验二：极限与连续

第一题：数列极限

In [1]= f[n」:=Sum[1/jA3,{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.

193207119,1.195160244,1.196531986,1.197531986,1.198283300,1.198862004,1.199

317170,1.199681602,1.199977898,1.200222039,1.200425580,1.200597048,1.200742

842,1.200867842,1.200975822,1.201069736,1.201151926,1.201224264,1.201288264

,1.201345159,1.201395965,1.201441518,1.201482521,1.201519558}

In [2]= ListPlot[x n,PlotStyle Poi ntSize[0.02]]

Out[2]=

Graphics

第二题：递归数列

In [3]= Clear[f];

f[1]=1;

f[n_:=f[ n]=N[(f[ n-1]+3/f[ n-1])/2,20];

fn=Table[f[ n],{n, 30}]

Out[3]=

{1,2.0000000000000000000,1.7500000000000000000,1.7321428571428571429,1.73