Oresme's proof (from the 14th century).pic.twitter.com/xz6sstfcNg
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The divergence of the harmonic series has surprising consequences. For example, you can stack blocks over the edge of a table using the harmonic series and get an arbitrarily long "bridge".pic.twitter.com/eKQ9uTHnX3
could you explain why is 1+1/3+1/5+...>S/2
Each term is larger than the corresponding term in the S/2 series. 1 > 1/2, 1/3 > 1/4, and so on
Is the proof even accurate? Why do we have 1+1/3+1/5+...>S/2? It should be larger OR EQUAL here... Because it is possible to build two sequences (a_n) and (b_n) for which a_n < b_n , but both have the same limit.
1+1/3+1/5+...>= (1/2+1/4+...)+(1-1/2) > 1/2+1/4+...
Wasn't this on /r/math a little while ago?
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