This notebook will graph the sequence of terms, and the sequence of partial sums, associated with a series. First you run the next cell to define the function "graphSequences", then you go to the cell below it.

Off[General::"spell1"];
Clear[n, an, sn];
graphSequences[nMax_]:=Module[{},
an={a[1]};
sn={a[1]};
Do[AppendTo[an,a[i]];
AppendTo[sn,sn[[i-1]]+a[i]],
{i,2,nMax}];
aPoints=ListPlot[an,PlotStyle->Red];
aLine=ListPlot[an,PlotStyle->Red,Joined->True];
sPoints=ListPlot[sn,PlotStyle->Blue];
sLine=ListPlot[sn,PlotStyle->Blue, Joined -> True];If[nMax>19,xTicks=Automatic,xTicks=Range[nMax]];If[nMax>19,myPointSize=0.008,myPointSize=0.03];Magnify[Show[aLine,sLine,aPoints,sPoints,Prolog->PointSize[myPointSize],Ticks->{xTicks,Automatic},
PlotLabel->"(Subscript[a, n]) = "<>ToString[a[n],StandardForm],
AxesLabel->{"n",Style["(Subscript[a, n])",FontColor->Red] Style["(Subscript[s, n])",FontColor->Blue]}, 
PlotRange -> All, AxesOrigin ->{0,0}], 
1.5]]

Define the function for the general term a[n], then run the cell.  The integer argument to graphSequences[nMax] is the ending value of n.  The graphSequences function graphs the sequence of terms in red, and the sequence of partial sums in blue.

a[n_] =1/n; graphSequences[10]