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.
So isn't this series basically sigma of n for which n starts from 1 and ends at infinity? In this case, in my opinion, as every terms in this series is positive, this series can immediately be included in the 'comparison tests for convergence and divergence'. French mathematician Nicole Oresme has proved the divergence of the harmonic series 1/n by proving the divergence of a series which has lesser terms than that of the harmonic series. If, as what the numberphile people are saying, 1+2+3+4+... forever does equals to 1/12 doesn't this make the whole concept of comparison test flawed? Even if the Grandi's series which is 11+11+11... does actually equals to a half, the answer 1+2+3+4+.. forever does not make sense as it makes previous proofs and statements made in infinite series incorrect.
Also, i don't understand what the average partial sums are for. Why is there the need to average the partial sums? The average of the partial sums may converge towards a half but that doesn't mean anything that the 'nonaverage' (as in real) series converge towards a half...