Determine whether the sequence converges or diverges. If it converges find the limit.

Question

a_n=e^(-1/sqrt(n))

Apparently in converges and the limit is 1 but I'm not really sure how to do this type of problem with a limit of e^x

 

{n²e^-n}

Limit converges to 0? How?

 

 

Answer 1

n approaches infinity, so square root of n approaches infinity.

 

ratio -1/infinity approaches zero; e⁰ = 1.