Original statement:
I'm sure the n+4 in both the denominator and numerator have something to do with it, but if i make in the denominator a , wouldn't that then make it smaller the the LHS?
I'm suppose to prove
which means i need the inequality to make the RHS bigger than the LHS
That notation means as n approaches infinity, becomes arbitrarily close to 0. It is read the limit of as n approaches infinity is 0.
So given any , there exists an integer N for which, for all n>N.
In particular, if , there exists an N, such that for all n>N, , this means we clearly have the identity .
Thus for all n>N. Which is the definition of