Add new comment
-
Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.
Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!
How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?
Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.
PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.
As I thought, this is text book material. Whittaker & Watson: A Course of Modern Analysis, 4th ed. Chapter 2 example 6 has the sum for (1/2)log 2 which looks as if it is an exam question from 1908. And section 2.4 cites a reference to Dirichlet in 1837.
At each step in the sequence generation, one positive and two negative terms are created. Every partial sum has twice as many negative as positive terms. The claim is that none are omitted since the series is infinite, and yet at any partial sum step 1/3rd of the elements from the original series have been lost.
Infinity doesn't correct the problem as at every subsequent step the problem gets worse! An infinite number of terms does not mean ALL terms.