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Quotation

The number of partitions of 3, p( 3), is just 3 (3, 1 + 1 + 1, 1 + 2). But by the time you get up to 10, p( 10) = 42. And p( 50) = 204,226. ... === 1 + 2 + 3 + 4 + . . . = − 1/ 12 (Check out the proof in numerous sources.) In chapter 6 was that bizarre stuff from the first letter about divergent series that, Ramanujan had feared, might persuade Hardy he was destined for the lunatic asylum— the one where 1 + 2 + 3 + 4 + . . . unaccountably added up to − 1/ 12. On its face, that was ridiculous; yet it sought to give meaning to divergent series— which at first glance added up to nothing more revealing or precise than infinity. === Drop a needle onto a table finely scored by parallel lines each separated by the length of the needle and the chance of its intersecting a line is 2/ pi.