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).

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