Question3. $\sum_{n=1}^{\infty} \frac{5 n^{3}}{n^{4}+7}$

Studdy Solution
Determine the convergence or divergence of the original series. Since the harmonic series $\sum_{n=1}^{\infty} \frac{1}{n}$ diverges and the Limit Comparison Test shows that our series behaves like the harmonic series, the original series $\sum_{n=1}^{\infty} \frac{5n^3}{n^4+7}$ also diverges.
The series $\sum_{n=1}^{\infty} \frac{5n^3}{n^4+7}$ diverges.