Analysis Help: Lim SnTn is +Inf

[Zygotic Embryo]

Let (Sn) and (Tn) be sequences such that the lim Sn = +inf and lim Tn > 0

Then lim SnTn = + inf

 

[Hurkyl]

What is the question? And what work have you done on this problem?

 

[Zygotic Embryo]

A friend of mine, gave it to me.

I don't know where to start

 

[Zygotic Embryo]

its a statement

i need a proof

 

[matt grime]

what doyou know about sequences, and multiplication (or division) of sequences?

 

[Zygotic Embryo]

is it

Let M > 0

Select a real number m so that 0 < m < limTn.

There exists an N1 such that:
n>N1 implies Tn>m

Since limSn=+inf there exists an N2 such that
n>N2 implies Sn>(M/m)

Set N = max{N1,N2}.

Then n>N imples SnTn>(M/m)*m = M

 

[nocturnal]

I thought I recognized the wording you used for the statement of this theorem and its proof and sure enough, it is taken word for word out of the book "Elementary Analysis: the Theory of Calculus" by Kenneth Ross (pg 50-51). Its stated with proof as theorem 9.9

If you have the proof in front of you, why are you asking if that's it? Is there some part of the proof you don't understand?