It was gently pointed out to me by Ted Harding that my question was a
load of dingos' kidneys. What happened was that I left out a crucial
factor of 1/k.
Here's the question again, stated correctly this time.
(I think!!!)
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Please reply to me directly (rolf at math.unb.ca) rather than to the
list, since the question is completely R-free and I'm simply asking
this list because there are so many clever and knowledgeable people
on it.
Suppose that n_i, i = 1, 2, 3, ... are positive integers, and that
1 k
lim --- SUM n_i^j = nu_j < infinity
k --> infinity k i=1
for j = 1, 2, 3. Need it be the case that
1 k-1
lim --- SUM n_i * n_{i+1} exists?
k --> infinity k i=1
I can neither prove this, nor come up with a counter-example.
Can anyone help me out?
cheers,
Rolf Turner