We know that $0<\dfrac{2^n}{3^n(n+7)} < \left(\dfrac{2}{3}\right)^n$ for any $n\ge 1$. **Considering this fact, what does the direct comparison test say about $\displaystyle\sum\limits_{n=1}^{\infty }\dfrac{2^n}{3^n(n+7)}$ ?** [[☃ radio 3]]