Solution
= Solution
Add the supplied five-term <partial sum> to each side of the tail inequality. Since $1/6=600/3600$ and $1/5=720/3600$,
$$
\boxed{\frac{5869}{3600}<\sum_{n=1}^\infty\frac1{n^2}<\frac{5989}{3600}.}
$$
Numerically this is approximately $1.63028<\sum n^{-2}<1.66361$.