Let $S$ be the value of following infinite series:
\[
\sum_{n=1}^{\infty} \frac{1}{n^{4}} .
\]
In which of the following intervals must $S$ lie?
- $\left[\frac{\pi^{4}}{900}, \frac{\pi^{4}}{450}\right]$
- $[0.95,1.05]$
- $\left[\frac{\pi^{4}}{100}, \frac{\pi^{4}}{80}\right]$
- $\left[\frac{\pi^{4}}{2}, \pi^{4}\right]$
- The series diverges, so $S$ must be infinity.
