<s>[INST] How to evaluate the limit $\lim_{x \to \infty} \frac{2^x+1}{2^{x+1}}$ How to evaluate the limit as it approaches infinity
$$\lim_{x \to \infty} \frac{2^x+1}{2^{x+1}}$$
 [/INST] Hint:
$\displaystyle \frac{2^x + 1}{2^{x+1}} = \frac{2^x}{2^{x+1}} + \frac{1}{2^{x+1}} = \frac{1}{2} + \frac{1}{2^{x+1}}$
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