[R] (Off topic) Limit question.

Rolf Turner rolf at math.unb.ca
Wed Sep 21 23:35:24 CEST 2005

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

	  lim        SUM n_i^j = nu_j < infinity
     k --> infinity  i=1

for j = 1, 2, 3.  Need it be the case that

	  lim        SUM n_i * n_{i+1}     exists?
     k --> infinity  i=1

I can neither prove this, nor come up with a counter-example.
Can anyone help me out?


					Rolf Turner

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