Convergence and Divergence

[maeveoneill]

Is there a way(s) to determine whether a function is convergent or divergent simply by looking at it??

 

[Deleted member 4993]

Is there a way(s) to determine whether a function is convergent or divergent simply by looking at it??

What do you exactly mean by that? Did you mean series or function?

If give me a geometric series with r>1 (e.g. 2^n) - I can simply look at it and tell it is going to diverge.

If by function diverging - you mean definite integral - for some functions you can do that.

But almost all of those require calculating the limit (mentally at least).