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Solution: Using only the Archimedean property, give a direct ε -N verification of the convergence of the following sequences. (2)/(√n)+1/n+3

Question: Using only the Archimedean property, give a direct \(\varepsilon -N\) verification of the convergence of the following sequences.

  1. \(\left\{ \frac{2}{\sqrt{n}}+\frac{1}{n}+3 \right\}\)
  2. \(\left\{ \frac{{{n}^{2}}}{{{n}^{2}}+n} \right\}\)

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