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evinda

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I want to show that if $c_k=\frac{p_k}{q_k}$ the $k$-th convergents of the continued fraction $[a_0; a_1, a_2, \dots, a_n]$, then $q_k \geq 2^{\frac{k-1}{2}} (1 \leq k \leq n)$.

Could you give me a hint how we could show this? (Thinking)