# Nth term test & convergence

For a problem such as $$\sum$$ (1-3/n)^n with the sum going from 1 to infinity, the textbook shows to use the nth term test & that it diverges. However in a previous chapter the textbook had a theorem that said the limit of $$\sum$$ (1+x/n)^n will converge to e^x for any number x.

So I'm confused. Are they using convergence in a different context or what am I missing?

quasar987