S=sum of (-1)^n/n from 1 to infty

For why I named the post as so, here’s why

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  • @[email protected]
    4•5 months ago
    spoiler

    ln(2) because the Taylor series for ln(1+x) evaluated at x=1 is exactly this series.

    Good one. Thanks for posting!

    • @siriusmartOPM
      3•5 months ago

      yup thats the intended solution, im not really familiar with taylor series yet, but maybe for a person who knows taylor series would be able to see it right away

  • @quilan
    2•5 months ago

    There closest I was able to do on the fly was to show that the ::: pairwise sum has an integral of -ln(2)/2 ::: but that was pretty hand wavy. I’ll have to check how it’s actually done.

  • @[email protected]English
    1•5 months ago

    minus one plus a half minus a third plus a quarter… this converges to a value somewhere between 0 and -1, but I dont know how to get more precision without just running this out by hand a bunch more.