Limit as n approaches infinity:

[(n + 3)/(n + 1)]^n

How do I even start this?

2 answers

I would divide the polynomials...

lim (1+ 2/n + ...)^n= 1
Answer is e^2.

lim (n -> infinity) of [(n+3)(n+1)]^n
= lim (n -> infinity) of [1 + 2/(n+1)]^n

e = lim (x -> infinity) of [1 + 1/x]^x
e^2 = lim (x -> infinity) of [1 + 2/x + 1/x^2]^x