Originally posted by !~TONY~!
I am studying for a quiz tomorrow in Calc II and ran across I problem that I know we did in class but I don't know how to do it and didn't copy it down. (idiot, I know). The question is : Find whether the sequence (N + 1/ N) ^ N from N= 1 to infinity converges or diverges, and if it converges, where? The answer is e, but I didn't some mumbo jumbo that didn't work, and I don't even know if it's mathematically legal. Anyone know how to do this?
Well let's see. Just so that I'm sure. Is it [(n+1)/n]^n or is it [n+(1/n)]^n?
The first one just goes to 1. Since it can be rewritten
[1+(1/n)]^n which as n-> infinite goes to 1^n = 1.
So I don't suppose that's the version of it.
The second one clearly diverges. Again in the limit, 1/n -> 0, and so the sequence -> infinite^infinite .
You're sure the answer is e?
Maybe the question was a little different?
Well, that's my two cents. I'll differ to one of the mathematicians on the site if I'm missing something.