f[n_]:=Cos[2Pi/n]

Table[f[n],{n,1,20}]

FullSimplify[%]

f[n_]:=Sum[1/2^k,{k,1,n}]

f[{3,5,10,50}]

2^50

N[%,20]

Clear[g]

g[n_]:=N[f[n],n+5]

Table[g[n],{n,{3,5,10,50}}]

g[n_]:=f[n] 10^n

g[{3,5,10,50}]

a=3

Clear[x]

x[1]=1;x[n_]:=x[n]=(x[n-1]+a/x[n-1])/2

t=Table[x[n],{n,1,10}]

nt=N[t,100]

For[i=1,i≤10,i++,Print[nt[[i]]]]

N[Table[x[n+1]-x[n],{n,1,10}]]

nt2=nt*nt

{1.`99.69897000433602,4.`99.69897000433602,3.0625`99.69897000433602,3.000318877551020408163265306122448979591836734693877551020408163265306122448979591836734693877551020408163265306122448979591836734693879`99.69897000433602,3.00000000847267379690743339529456165503718758201548235406395526645135682075997579390986918733908697924913402495656568504753373344236196`99.69897000433602,3.000000000000000005982183422171789083280224723096843645478347909940608891391727028814125826072538465606438289940831636929812167860091534`99.69897000433602,3.000000000000000000000000000000000002982209874708914802069006752611708656519068861557466113530048558243127229480177260957367592695918253`99.69897000433602,3.000000000000000000000000000000000000000000000000000000000000000000000000741131311400946776801037944217930391571466131443630089640316741`99.69897000433602,3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001`99.69897000433602,2.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995969848`99.69897000433602}

For[i=1,i≤10,i++,Print[nt2[[i]]]]

a=21

Clear[x]

x[1]=1;x[n_]:=x[n]=(x[n-1]+a/x[n-1])/2

t=Table[x[n],{n,1,10}];

nt=N[t,100];

For[i=1,i≤10,i++,Print[nt[[i]]]]

Table[Print[N[x[n+1]-x[n]]],{n,1,10}];

nt2=nt*nt;

For[i=1,i≤10,i++,Print[nt2[[i]]]]

x[1]=1

For[i=1,i≤10,i++,x[i+1]=(x[i]+a/x[i])/2];

t=Table[x[i],{i,1,11}];

nt=N[t,100];

nt2=nt*nt;

For[i=1,i≤10,i++,Print[nt2[[i]]]]

g1=ContourPlot3D[(x+1)^2/1+y^2/4+(z-1)^2/9==1,{x,-4,2},{y,-3,3},{z,-3,5}]

g1a=ParametricPlot3D[{-1+Sin[t]Cos[p],2*Sin[t]Sin[p],1+3Cos[t]},{t,0,Pi},{p,0,2Pi}]

g2=Plot3D[{-x-y-Sqrt[14],-x-y+Sqrt[14]},{x,-4,2},{y,-3,3}]

Show[g1,g2,BoxRatios->Automatic,PlotRange->All]

Show[g1a,g2,BoxRatios->Automatic,PlotRange->All]

Graphics3D[Cone[]]

Graphics[Circle[]]

Plot3D[Sqrt[x^2+y^2],{x,-1,1},{y,-1,1}]

Plot3D[-5Sqrt[x^2+y^2],{x,-1,1},{y,-1,1},RegionFunction->Function[{x,y,z},x^2+y^2<1],BoxRatios->Automatic]

ParametricPlot3D[{r*Cos[t],r*Sin[t],-5*r},{r,0,2},{t,0,2Pi},BoxRatios->Automatic]