SetOptions[ListPlot,PlotMarkers->{Automatic,Medium}];

ListPlot[Table[{n,1},{n,1,10}]]

ListPlot[Table[{n,n},{n,1,10}]]

ListPlot[Table[{n,1/n},{n,1,10}]]

ListPlot[Table[{n,n/(n+1)},{n,1,10}]]

ListPlot[Table[{n,Cos[n Pi/6]},{n,1,10}]]

Show[
ListPlot[{Table[1/n^2,{n,1,10}]},PlotRange->{0,1}],
Plot[1/x^2,{x,1,10},PlotRange->{0,1}]
]

Show[
ListPlot[{Table[1/n^2,{n,1,10}]},PlotRange->{0,1}],
Plot[1/x^2,{x,1,10},PlotRange->{0,1}],
DiscretePlot[1/x^2,{x,1,10,1},ExtentSize->Left,PlotRange->{0,1}]
]
Show[
ListPlot[{Table[1/n^2,{n,1,10}]},PlotRange->{0,1}],
Plot[1/x^2,{x,1,10},PlotRange->{0,1}],
DiscretePlot[1/x^2,{x,2,10,1},ExtentSize->Left,PlotRange->{0,1}]
]

N[Pi^2/6]

f[x_]:=1/Sqrt[x];
Show[
ListPlot[{Table[f[n],{n,1,10}]},PlotRange->{0,1}],
Plot[f[x],{x,1,10},PlotRange->{0,1}],
DiscretePlot[f[x],{x,1,10,1},ExtentSize->Right,PlotRange->{0,1}]
]
Show[
ListPlot[{Table[f[n],{n,1,10}]},PlotRange->{0,1}],
Plot[f[x],{x,1,10},PlotRange->{0,1}],
DiscretePlot[f[x],{x,1,10,1},ExtentSize->Left,PlotRange->{0,1}]
]

f[n_]:=(-1)^n/n
ListPlot[Table[f[n],{n,1,20}]]
Show[
ListPlot[Table[Sum[f[k],{k,1,n}],{n,1,20}],Joined->True],
Plot[-Log[2],{x,1,20},PlotStyle->{Orange,Dashed}]
]