# Homework Help: Limit that equals e^2

1. May 3, 2012

### arl146

1. The problem statement, all variables and given/known data
the problem asks to find the limit of the sequence an = (1+(2/n))^n

2. Relevant equations
?

3. The attempt at a solution
i saw a solution where they said:

lim{n→∞} [1+(2/n)]^n
= lim{n→∞} [1+(2/n)]^[(n/2)2]
= [lim{m→∞} [1+(1/m)]^m]^2, where m = n/2
= e^2

am i supposed to just know that [1+(1/m)]^m = e ? or am i supposed to show it for this problem

2. May 3, 2012

### Office_Shredder

Staff Emeritus
The limit as m goes to infinity is e. Either you're supposed to know this or you're supposed to prove it... what is the definition of e that you are using?

3. May 3, 2012

### Staff: Mentor

Your book probably has an example where they let y = (1 + 1/m)^m, then take ln of both sides.

After that they take the limit and use L'Hopital's Rule. There's a little more to it than I've said, but that should give you something to look for.

4. May 3, 2012

### arl146

i dont know what the definition of e is that im using ...

i just dont know in my hw if i could just get to that point and then say,oh yea [1+(1/m)]^m = e and that be it. or if i actually have to show it. i guess it doesnt hurt to show it. ill try it out

5. May 4, 2012

### Staff: Mentor

You don't need the definition of e. Use what I said in post #3.