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ISI2021-MMA: 16

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The series $$ \sum_{n} \frac{3 \cdot 6 \cdot 9 \cdots 3 n}{7 \cdot 10 \cdot 13 \cdots(3 n+4)} x^{n}, \quad x>0 $$

  1. converges for $0<x \leq 1$ and diverges for $x>1$
  2. converges for all $x>0$
  3. converges for $0<x<\frac{1}{2}$ and diverges for $x \geq \frac{1}{2}$
  4. converges for $\frac{1}{2}<x<1$ and diverges for $0<x \leq \frac{1}{2}, x \geq 1$.
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