Question
Use the limit comparison test to determine whether the series converges or diverges.$\sum_{n=1}^{\infty} \frac{5 n+1}{3 n^{2}},$ by comparing to $\sum_{n=1}^{\infty} \frac{1}{n}$
Step 1
In this case, we are comparing the series $\sum_{n=1}^{\infty} \frac{5 n+1}{3 n^{2}}$ to the series $\sum_{n=1}^{\infty} \frac{1}{n}$. So, we need to find the limit as n approaches infinity of $\frac{\frac{5 n+1}{3 n^{2}}}{\frac{1}{n}}$. Show more…
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