Determine whether the series sum of 1/n^2 converges

Problem: Determine whether the series $\sum_{n=1}^{\infty} \frac{1}{n^2}$ converges or diverges.

Steps

1. Identify the series as a $p$-series
   $$\sum_{n=1}^{\infty} \frac{1}{n^p} \quad \text{where } p = 2$$
2. Compare the exponent $p$ to the threshold value $1$
   $$p = 2 > 1$$
3. Apply the $p$-series test
   $$\sum_{n=1}^{\infty} \frac{1}{n^2} \text{ converges}$$