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The series converges,1 and Euler found its sum in 1734.2
1 Its partial sums are bounded: .
2 The problem was posed by Pietro Mengoli in 1650.
The series $\sum_{n \ge1} n^{-2}$ converges,\footnote{Its partial sums
are bounded: $\sum_{n=1}^{N} n^{-2} < 1+\sum_{n=2}^{N}
\frac{1}{n(n-1)} =2-\frac{1}{N}$.} and Euler found its sum in
1734.\footnote{The problem was posed by Pietro Mengoli in 1650.}
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