MathDB

5

Part of 1974 Poland - Second Round

Problems(1)

t = lim sum_{j=1}^N q^{n_j}.

Source: Polish MO Second Round 1974 p5

9/8/2024
The given numbers are real numbers q,t∈⟨12;1) q,t \in \langle \frac{1}{2}; 1) , t∈(0;1⟩ t \in (0; 1 \rangle . Prove that there is an increasing sequence of natural numbers nk {n_k} (k=1,2,… k = 1,2, \ldots ) such that t=lim⁡N→∞∑j=1Nqnj. t = \lim_{N\to \infty} \sum_{j=1}^N q^{n_j}.
limitalgebraSequence