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
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
Feb11-12, 04:12 PM
Sci Advisor
P: 6,040
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: 6,040
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