Fun with roots and series

Came across this bit of high-school math with series/roots:

It’s straightforward, lots of paper-and-pen solutions in that thread.

Something like Wolfram Mathematica makes it much easier:

The above shows a “sanity-checking” approximate solution with one term, followed by the correct solution.

It’s equally straightforward, spent 5-10 minutes to let off steam at the end of the day πŸ™‚

Incidentally, WolframAlpha is able to get you the basic series solution too:

So, we’re really drowning in resources right now (which is balanced, I suppose by drowning even harder in distractions).

“Digits of Pi”

Saw a recent post on how “digits of Pi add up to 666” and decided to investigate.

These days I’m finding Mathematica super-useful for stuff like this, so:

That does NOT add up.

But this does:

Okay, this is stretching things a bit. It certainly sounds fun to say “the first 144 digits of Pi add up to 666” and then go on to show how 144 is a cool number (which it is, so is 1440).

But it’s less fun to say “the first 144 digits of Pi except for the first one add up to 666″, which is the truth here.