To evaluate the limit of the series, we evaluate the limit to infinity of the expression inside the sum, as following:
[tex]\lim _{n\to\infty}\frac{3n^3}{15n^4+5}[/tex]
Since the denominator is one degree higher than the numerator, we can conclude that:
[tex]\lim _{n\to\infty}\frac{3n^3}{15n^4+5}=0[/tex]
Answer: Option 1
