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I’m in a pub with Katie Steckles, about to order infinitely many drinks.

We’re taking requests. If anyone has a favourite infinite series: let us know now!

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Arne Tobias Malkenes Ødegaard

They're more typically referred to as sequences, and they're not very concrete, but I love Specker sequences, bounded and strictly increasing sequences of computable numbers which do not converge to a computable real. Some of them also have nice series representations.

Frank Gevaerts

Not an infinite series (although you can use one to get at the numbers involved), but have you ever noticed that acceleration due to gravity on earth is very close to π² m/s²? Very much related to one early candidate for the definition of the metre being the length of a pendulum with a period of 1s.

Patrick W. Gilmore

Is it sad that my favorite infinite series is the integers?

Bruce Grembowski

While the Fibonacci series is one of my favorites, 1- 1/3 + 1/5 - 1/7 + ... = pi/4 is right up there.

Timur Sultanov

1/n^2 would be mine... Because pi^2/6 is just such a pleasing result...

Daniel Brahneborg

If you order 1+2+3+... drinks, will you have to give 1/12th drink back to the bartender?

mooncow

That's one of my favourites too. Plus you can imagine a follow-up, when the beers are nearly finished, and the bartender comes along and asks "Would anyone like another?". The first logician says, "I don't know", and the second logician says, "I don't know", and the third logician says "No, thank you".

Christian Leichsenring

If you order infinitely many drinks, you must have an infinite amount of money in which case you should be hitting a casino, not a bar. Not only because the drinks there are free but also because you can play a roulette strategy that's guaranteed to make you money. Which, arguably, you already have enough of but then again, if capitalism has taught us anything it's that you never have enough money.

Christian Leichsenring

Oh and because the infinite series so far were all a bit, no offense, basic, how about w-1/2+1/8w^(-1)-1/4w^(-2)+(15)/(128)w^(-3)+0w^(-4)-(47)/(1024)w^(-5)+..., which is the Laurent series that maps the exterior of the unit disk to the exterior of the Mandelbrot set.

Matt Parker

Those are interesting! I’ve put them on my video ideas list.

Matt Parker

I think it’s a conspiracy on a universal scale.

Matt Parker

Not at all. You can always count on the integers.

Matt Parker

We considered doing that one in the pub but decided taking beer back out would get a bit messy.

Matt Parker

I saw this too late! I wish we had filmed that!

Matt Parker

If this video goes well, we may go back for more mathematicians in the pub videos.

Matt Parker

Solid point. But casinos are way less happy when mathematicians show up with a video camera.