Even though we are looking at infinite sets, it seems to me that I
should approach this as I have other practice problems in this
section.  That means that I need to start by getting the dot product
of these two vectors.  Algebraically, this is simple since all
elements in x are 1's, so I only need to sum the elements in y and I
can do that with the formula sum(1,2,3...n) = n(n+1)/2.

To find cos(theta), I need to get the magnitude of the two vectors,
multiply them times cos(theta) and set that equal to n(n+1)/2, then
solve for cos(theta) by dividing by the magnitudes and using the
inverse cos function to obtain theta.

So far, much of this looks like other practice problems but this is
the first one that used infinite sets.  Unless someone can tell me
that my procedure so far has a flaw in it, it seems as though this
should work for this problem just as it has for other problems.

Yet trying to work with the magniture of y has not panned out.  From
Calc II, I have the formula n(n+1)(n+2)/6 as the sum of the squares of
the sequence 1^2+2^2+3^2...+n^2.  So it looks to me like I need to
take the square root of this to get the y magnitude and then multiply
it by the sq root of the sum of the terms in the x vector which would
simply be sqrt(n).  Those two magnitudes times cos(theta) would then
be set equal to n(n+a)/2.  Then I would divide through and take the
arccos of the result.

But I keep messing something up.  The answer is supposted to be pi/6.
I cannot see how that result is achieved.

Did I make some obvious error in this process?  Some not so obvious
error?  Or does this look right and I just screwed up the algebra?