Need serious help on a proof:

Show that if lim(an/n) = L where L>0, then lim an (n approaches inf) = inf.

Thanks guys.

Printable View

- November 1st 2006, 07:33 PMJimmyTA limit
Need serious help on a proof:

Show that if lim(an/n) = L where L>0, then lim an (n approaches inf) = inf.

Thanks guys. - November 1st 2006, 09:25 PMCaptainBlack
- November 2nd 2006, 11:26 AMJimmyT
I don't understand what you mean when you say "rearrange" it by "arbitrarily small amounts."

- November 2nd 2006, 12:15 PMPlato
- November 2nd 2006, 01:34 PMCaptainBlack
Of course you are right, I don't mean what I say at all do I:mad: .

What I do mean is that for every epsilon>0, there exists an N such that

for all n>N:

-epsilon< (a_n)/n-L <epsilon

so:

nL-n epsilon< a_n < nL + n epsilon,

or:

n(L-epsilon) < a_n < n(L+epsilon)

so if we choose a small enough epsilon, as n-> infnty a_n is trapped between

two sequences both of which go to infinity.

RonL