infinite series

Approximating a function with a divergent series.

If you ignore exponentially small terms they can come back to bite you.

How a question about rainbows led to an entire field of mathematics.

Scientists have calculated the decimal digits of the number pi to a record 62.8 trillion places.

This problem about an infinite sum has a surprising answer.

How to write a sum that's infinitely long.

What is 1-1+1-1+1-1+...? How infinite sums challenge our notion of arithmetic.

What do you get when you add up all the natural numbers 1+2+3+4+ ... ? Not -1/12! We explore a strange result that has been making the rounds recently.

The number pi can be expressed beautifully in terms of infinite sums. For practical purposes though, these sums are rather disappointing: they converge slowly, so you need to sum a large number of terms to get accurate estimates of pi. Here's a clever way to make them converge faster.

Two computer geeks claim to have calculated the number pi to 5 trillion digits — on a single desktop and in record time. That's 2.3 trillion digits more than the previous world record held by the Frenchman Fabrice Bellard.

Victoria Gould has always known she would be an actor, and went straight from studying arts at school to running her own theatre company. But she eventually had to come clean about her guilty secret - she loves maths - and has since managed to combine a career as a research mathematician and teacher with a successful acting career on television and in theatre. She tells Plus why she needs to use both sides of her brain.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.