Register to reply

Lim of An=n^2*exp(-sqrt(n))

by oferon
Tags: ann2expsqrtn
Share this thread:
Feb11-12, 03:28 PM
P: 30
Hi all, my problem regards this limit:


Obviously equals 0, but I can't find how to show it.
Tried the squeeze theorem (coudn't find any propriate upper bound)
Ratio test won't seem to work..
I do realize the reason for that is that the set approaches 0 starting at heigher n's..

Anyway.. how can I prove convergence and find the limit in a formal way? thanks!
Phys.Org News Partner Science news on
Mysterious source of ozone-depleting chemical baffles NASA
Water leads to chemical that gunks up biofuels production
How lizards regenerate their tails: Researchers discover genetic 'recipe'
Feb11-12, 04:12 PM
Sci Advisor
P: 6,058
Simple method: Let m=√n, so the problem is limit m -> ∞ m4/em.

em = 1 + m + m2/2! + m3/3! + m4/4! + m5/5! + .... It is obvious from the 5th term on the denominator of the fraction swamps the numerator.
Feb11-12, 05:56 PM
P: 30
I've tried changing variables like you did and got m4/em, which does seem nicer..
But is using taylor expansion the only way to solve here?
I'm pretty sure that's not what the course staff expected us to do..

Feb12-12, 05:53 PM
Sci Advisor
P: 6,058
Lim of An=n^2*exp(-sqrt(n))

Have learned L'Hopital's rule?
If so, use that. Take 5 derivatives of the numerator and the denominator and get 0/em.

Register to reply

Related Discussions
Prove that the limit of sin(sqrt(x+1))-sin(sqrt(x-1)) at infinity doesn't exist Calculus & Beyond Homework 10
Prove series is divergent (sqrt(n+1) - sqrt(n))/sqrt(n) Calculus & Beyond Homework 5
Iterative square root? sqrt(2+sqrt(2+sqrt(... General Math 6
Is there a way to show that sqrt(2)+sqrt(3)+sqrt(5) is algebraic over Q? General Math 4
Proof that sqrt(6)-sqrt(2)-sqrt(3) is irrational General Math 10