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Maths in a Minute: The Harmonic Series
The harmonic series look simple. But, perhaps breaking your intuition, grows without bound!
Content about “ infinite series
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Maths in a Minute: the Leaning Tower of Lire
The surprising physics of stacking coins.
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Proof by chocolate
How to sum an infinite series using chocolate.
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The Fields Medals 2022: James Maynard
James Maynard has won a field medal for his work in number theory. He told us how he went from a fascination with numbers as a young child to making spectacular contributions to number theory.
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Maths in a minute: Asymptotic expansions
Approximating a function with a divergent series.
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The power of small things: Resurgent asymptotics
If you ignore exponentially small terms they can come back to bite you.
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Stokes's phenomenon: An asymptotic adventure
How a question about rainbows led to an entire field of mathematics.
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The Basel problem
This problem about an infinite sum has a surprising answer.
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Maths in a minute: Writing infinite sums
How to write a sum that's infinitely long.
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Infinity or -1/12?
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.
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How to add up quickly
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.