Sunday, 24 September 2017

calculus - Not using Taylor series or Maclaurin series, prove frac1sqrt1x2=1+frac1cdot32cdot4x2+frac1cdot3cdot52cdot4cdot6x4+cdots

I’m trying to find a proof of
11x2=1+1324x2+135246x4+,


which doesn’t need Taylor or Maclaurin series, like the proof of Mercator series and Leibniz series.
I tried to prove it by using calculus, but I couldn’t hit upon a good proof.

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