ListPlot[Table[1+1/n,{n,100}],PlotRange->{{0,100},{0,2}}]

ListPlot[Table[Cos[n/4]/n,{n,100}]]

ListPlot[Table[n*Sin[n/4]/4,{n,100}]]

Show[ListPlot[Table[1+1/n,{n,100}],PlotRange->{{0,100},{0,2}}],Plot[1,{n,0,100}]]

Show[ListPlot[Table[Cos[n/4]/n,{n,100}]],Plot[0,{n,0,100},PlotStyle->{Thick,Red}],Plot[1/n,{n,0,100},PlotStyle->{Thick,Purple}],Plot[-1/n,{n,0,100},PlotStyle->{Thick,Purple}]]

ListPlot[Table[((-1)^n)((2n+1)/(n^2)),{n,100}]]

ListPlot[Table[((-1)^n)((2n+1)/n),{n,100}]]

G[1]=Sqrt[2];
G[n_]:=Sqrt[2*G[n-1]]
ListPlot[Table[G[n],{n,100}]]