Trying to Find Limits directly from the Definition of a Limit of a Sequence

[The Student]

In class we were only taught to prove a limit when the limit was already given. How do I use n > N

[an - L] < ɛ to find the limit for n/(n+1)? I have no idea how I can find L with this definition.

 

[stapel]

In class we were only taught to prove a limit when the limit was already given. How do I use n > N

[an - L] < ɛ to find the limit for n/(n+1)? I have no idea how I can find L with this definition.

I don't think anybody "finds" the limit from the definition. They find it by other methods, or at least guess at it. They use the definition to prove that they're right. In this case:

Use algebra (or graphing, or whatever) to find what the limit is (or, at least, what you think it is). Then do the proof.

 

[The Student]

I don't think anybody "finds" the limit from the definition. They find it by other methods, or at least guess at it. They use the definition to prove that they're right. In this case:

Use algebra (or graphing, or whatever) to find what the limit is (or, at least, what you think it is). Then do the proof.

Oh great, that's what I was hoping to be the case - thanks!