Find Limit of Sequence: an = (1/(e^(4n)+n^2))^1/n

[TWM]

Find the limit of the sequence whose terms are given by

an = ( [1/(e^(4n)+n^2)] )^1/n

I am not really sure how to approach this problem.

thanks!

 

[Amauta2K]

Try the binomial expansion of denominator and apply the limits to each term (don't forget that you always can use the L'Hopital rule for those limits). I guess the that the limit is 1/e^4.