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ShadowSword · Busted!

Recently I watched the NOVA episode (a PBS show) on Newton called Newton's Dark Secrets. They mention that he enjoyed calculating logs to 50 decimal places for fun and showed this image as they said it. Does anyone know how this method works? Is this just the summation version of log(x) for n=1 to however high he wanted to go or is it something different?

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Trojan Horse · Daedalian Member

It looks like he's taking the sum of 1/(n*10^n), for all odd n.

Assuming my brain is functioning, he is getting (1/2)*ln(11/9). (I'd explain how I got that, but it's 5:30 in the morning here, and I'm still groggy. Ecstatic Happiness

)

ShadowSword · Busted!

Interesting. I did notice the decimals were the odd fractions but that was as far as I got.
_________________
"Heads you're good, tails you fail" says my fortune cookie

Lepton* · Guest

I taught (the general) form of this to my grade 11 calculus class last month. This is definitely a cherry-picked easy example! But the convergence is pretty fast.