I need to find $\lim_{x \to \infty} \frac{x}{2^{2x}}$ (and I think that it is 0) with the help of Bernoulli's inequality, which states that $(1 + x)^n \ge 1 + nx$ for all $x \ge -1$. However, I struggle to make sense of how I should use it to find a limit. A hint would be appreciated.
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1You should edit your question to include what Bernoulli's inequality is. That way your question will be more self-contained – user6247850 Jun 15 '23 at 13:32
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2Hint: $2^{2x} = ((1+1)^x)^2$. – See also https://math.stackexchange.com/a/3401545/42969 – Martin R Jun 15 '23 at 13:40
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Also here: https://math.stackexchange.com/a/56298/42969 – Martin R Jun 15 '23 at 13:47