Test the series for convergence or divergence. $$\sum_{n=1}^\infty \frac{3^n n!}{8 \cdot 13\cdot 18\cdots (5 n+3)} .$$

Use the Select Ratio Test Root Test and evaluate:

$\displaystyle \lim_{n \to \infty}$ $=$ . (Note: Use INF for an infinite limit.)

Since the limit is Select finite greater than 1 equal to 1 less than 1 greater than 0 equal to 0 , Select the series diverges the series converges conditionally the series converges absolutely we know nothing .