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Consider the sequence \((u_n)\) defined for \(n \ge 1\) by \(u_n = \dfrac{n+1}{n^2 + n}\).
  1. Show that using the quotient rule directly leads to an indeterminate form.
  2. Show that for all \(n \ge 1\), \(u_n = \dfrac{1+\frac{1}{n}}{n(1+\frac{1}{n})}\).
  3. Deduce the limit of the sequence \((u_n)\).

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