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Prove It $\displaystyle \frac{2n + 1}{n + 1} = \frac{2n + 2}{n + 1} - \frac{1}{n + 1}$
$\displaystyle = \frac{2(n + 1)}{n + 1} - \frac{1}{n + 1}$
$\displaystyle = 2 - \frac{1}{n + 1}$.
What happens as $\displaystyle n \to \infty$?