Solution Using Mathematica

Since the summation is very difficult to evaluate by hand, let's call Mathematica to the rescue. The following three Mathematica commands (typed at your Mathematica prompt), produce a floating-point approximation to the numeric value of .

Needs["Symbolic Sum"]

vs= Sum[(((2*i/(2*n+1))*(1/n)/sqrt(((2*i)/(2*n+1)-1/2)^2 + (1/2)^2)),i=-n..n]

N[%]

Remember the result that you obtain as you read the next section, which describes a continous model for the problem at hand, and expesses the scaled potential as a 1-D integral.