Thread
:
Lim of An=n^2*exp(-sqrt(n))
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mathman
#
2
Feb11-12, 04:12 PM
Sci Advisor
P: 6,112
Simple method: Let m=√n, so the problem is limit m -> ∞ m
^{4}
/e
^{m}
.
e
^{m}
= 1 + m + m
^{2}
/2! + m
^{3}
/3! + m
^{4}
/4! + m
^{5}
/5! + .... It is obvious from the 5th term on the denominator of the fraction swamps the numerator.