Such proof uses [[Bernoulli's Inequality]]. We usually take $x>1$ wlog since $x<1 \implies \frac{1}{x}>1$. When sequences we take $x_{n}=f(h_{n})$ and use [[Sandwich Rule]] on $(h_n)$. ### Examples - [[Criterion for Convergence of Geometric Sequence]]. - [[x to the power of the reciprocal of n converges to 1 for any positive x]]. - [[n to the power of the reciprocal of n converges to 1]].