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

mathman

Simple method: Let m=√n, so the problem is limit m -> ∞ m⁴/e^m.

e^m = 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.

mathman Recognitions: Science Advisor	Simple method: Let m=√n, so the problem is limit m -> ∞ m⁴/e^m. e^m = 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.