# Nth term test & convergence

1. Apr 22, 2008

### kuahji

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?

2. Apr 22, 2008

### quasar987

It is (1+x/n)^n that converges to e^x, not the sum of that.

And actually, you can use this fact to show that the series in your problem diverges. You know that (1-3/n)^n converges to e^{-3}, which is not 0, hence the series diverges.

Last edited: Apr 22, 2008
3. Apr 23, 2008

### kuahji

Thanks for the reply. I see that I obviously got confused ^_^.