Add new comment

I saw a demonstration of this sum recently. It went like this:
the periods indicating a continuation to infinity, it is assumed that:

Then again, the alternating harmonic series converges to ln2 but by rearranging the terms in the equation, it also converges to (ln2)/2 and (ln2)/4 and so forth. The problem in your reasoning is that you take a partial sum as reference. I know that it's counter-intuitive just like 0.00000...1= 0 but the reason it gives that result is only because the sum is infinite. The moment it becomes finite, these results all go wrong.

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.
  • 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.