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An investor places \(\dollar1,000\) in a savings account with a yearly compound interest rate of \(5\pourcent\). Let \(u_n\) be the amount of money in the account after \(n\) years.
Calculate the values of \(u_1\) and \(u_2\).
Express \(u_n\) in terms of \(n\).
Determine the limit of the sequence \((u_n)\) as \(n \to +\infty\) and interpret the result.
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