Hello,

how can I prove that the set E(x) = { (1+x/n)^n} is bounded ? (n is a natural number and x is a positive real number)

I had already proven that the set has no largest element using a consequence of the AGM inequality.

I also know from calculus that the limit of (1+x/n)^n is actually e^x . but this is of no use to me, since e^x is not yet defined in my analysis course.

any help would be much appreciated.