Thread: Converging Sequence!! AKA Infinite Series!!

Question:

Show that the sequence is convergent by computing its limit when n -> ∞

a(n) = (e^-n)/[1-n^(1/n)]


Related Equations:

lim [n -> ∞] a(n) = L


My Attempt:

I tried using l'hopitals rule however it does not work.
Any suggestions???

Originally Posted by olyviab1

Question:

Show that the sequence is convergent by computing its limit when n -> ∞

a(n) = (e^-n)/[1-n^(1/n)]


Related Equations:

lim [n -> ∞] a(n) = L


My Attempt:

I tried using l'hopitals rule however it does not work.
Any suggestions???

Hint: since clearly ,we get , and thus:


, and this last limit is zero by L'H. rule ... and yes, I know the denominator is twisted, but it never minds.

Tonio