MATH 132 -- Calculus for Physical and Life Sciences 2
April 8, 2005
The alternating harmonic series is . Question: Does
this converge?
Here are some of the partial sums:
Here's another way to visualize what the partial sums are doing. The plot
shows the partial sum values for N = 1 .. 50. Note that they seem to be
oscillating back and forth around roughly .69 ...
> | SList:=[seq([N,evalf(add((-1)^(n+1)/n,n=1..N))],N=1..50)]: |
> | with(plots): |
> | A:=plot(SList,style=point,color=red): |
> | B:=plot(SList,color=blue): |
> | display(A,B); |
So it looks like this series does converge to a number approximately .6931 ... Does this look familiar?
> | evalf(ln(2)); |
> |