Editing Euler–Maclaurin formula (section)

===The Basel problem===
The [[Basel problem]] is to determine the sum
<math display=block> 1 + \frac14 + \frac19 + \frac1{16} + \frac1{25} + \cdots = \sum_{n=1}^\infty \frac{1}{n^2}. </math>

Euler computed this sum to 20 decimal places with only a few terms of the Euler–Maclaurin formula in 1735. This probably convinced him that the sum equals {{math|{{sfrac|''π''<sup>2</sup>|6}}}}, which he proved in the same year.<ref>{{cite book
 | last = Pengelley | first = David J.
 | arxiv = 1912.03527
 | contribution = Dances between continuous and discrete: Euler's summation formula
 | location = Washington, DC
 | mr = 2349549
 | pages = 169–189
 | publisher = Mathematical Association of America
 | series = MAA Spectrum
 | title = Euler at 300
 | year = 2007}}</ref>