Again Computing limits

Calculus Level pending

Let \(\{a_n \}\) be a sequence of real numbers such that \(e^{a_{n}}+ na_{n}=2\) for all positive integers \(n\). Compute the limit

\[\lim_{n \to \infty} n(1-na_{n})\]

Enter 5555 as your answer if the limit does not exists.

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