# [R] (Off topic) Limit question --- corrected!!!

From: Rolf Turner <rolf_at_math.unb.ca>
Date: Thu 22 Sep 2005 - 21:40:33 EST

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@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

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