Erdős problem 349

For $0 < \alpha \le 1$ and any $t > 0$, $(t, \alpha)$ is not a good pair: every term $\lfloor t\alpha^n\rfloor$ lies in the finite interval $[0, \lfloor t\rfloor]$ (since $\alpha^n \le 1$), so every subset sum is bounded by the constant $\sum_{i \in [0,\lfloor t\rfloor]} i$, and no large integer can be a subset sum. A partial result on the open Erdős Problem 349, complementing the $2 < \alpha$ and integer-coefficient cases.