Formal definition of a sequence limit which tends to infinity

[harmonie_Best]

Homework Statement

hey there I have been given a question that asks me to define a sequence Xn which tends to infinity that has a limit that is infinity! I am so cofused. I would assume to use an adapted version of the epsilon delta condition?

Homework Equations

It's for Analysis!

The Attempt at a Solution

I attempted :
For all E > 0, there exists a delta >0 s.t. 0<!x!<delta then ?

Thanks!

 

[Mark44]

Homework Statement

hey there I have been given a question that asks me to define a sequence Xn which tends to infinity that has a limit that is infinity! I am so cofused. I would assume to use an adapted version of the epsilon delta condition?

Homework Equations

It's for Analysis!

The Attempt at a Solution

I attempted :
For all E > 0, there exists a delta >0 s.t. 0<!x!<delta then ?

Thanks!

There is no delta in the definition of convergence for a sequence that converges to a finite number. So for a sequence {a_n} that converges to L, the definition says that there is some number N such that |a_n - L| < epsilon, for all n >= N.

For a sequence whose limit is infinite, neither delta nor epsilon play a role in the definition. For this type of sequence, the definition is: For any large number M, there is a number N such that a_n > M for all n >= N.

The main idea here is that no matter how large a number M someone picks, there is an index N so that all the terms in the sequence past that index are larger than M.