What does it mean if the product of the solutions of a sequence converges to 0?

Question

agent0smith · Answer

Wouldn't that mean the terms of the sequence also eventually converge to zero? Since the limit of a product is the product of the limits.

darkprince14 · Answer

I took the limit of the sequence, and it has a nonzero value

darkprince14 · Answer

The product will be zero given certain conditions for the initial value of the sequence. Does that mean that, given these certain conditions, the limit of the sequence will also be 0?

agent0smith · Answer

What is the sequence? It sounds like you have a lot more information than we do

darkprince14 · Answer

$$x_n = \frac {q}{p + x_n ^\nu}$$
this equation where p, q and v are natural numbers.
The condition was p >  q-1

agent0smith · Answer

So people can read it $$\Large x_n = \frac {q}{p + x_n ^\nu}$$

This doesn't make a lot of sense to me. It shows xn as a function of itself.

darkprince14 · Answer

it was equal to x_(n+1). sorry. my bad.

darkprince14 · Answer

$$\Large{x_{n+1} = \frac{q}{p + x_n^\nu}}$$

agent0smith · Answer

It seems like with the above conditions, the terms should always eventually converge to zero.

darkprince14 · Answer

Oh so that's is what it is for. thanks :)

agent0smith · Answer

Actually I guess it does depend on what you choose the first x as... when I pick something like x=0.1, it doesn't approach zero