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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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