- #1
Isaac Wiebe
- 6
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Homework Statement
lim (3/n)^(2n)
n→ ∞
Homework Equations
L'hopital's rule: lim F(a)/G(a) is indeterminate form, then the limit can be written as lim F'(a)/G'(a)
x → a x→ a
The Attempt at a Solution
lim e^[ln(3/n)^(2n)] = lim e^(2n * ln(3/n))
n→ ∞ n → ∞
2n * ln(3/n) =
[2 * ln(3/n)] / (n^-1 )
and applying L.h., [2 * (n/3) * (-3/n^2)]/(-n^-2)
reduces to, 2 * n, and clearly, plugging in n = infinity is wrong. Where did I go wrong, and what can I do to fix this problem?
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