1

Why do we have $\lim \sqrt {2 - \sqrt {2 + \sqrt {2 + \sqrt 2 ...}}} (1/2)^n = \pi $ ?

Here $...$ means repeating $n$ times.

I assume it comes from repeated half-angle formulas.

Is this the case ? And if so, is there another way to prove the identity too ???

mick
  • 15,946
  • The real question is , why havent I seen this before :) I have only seen the similar vieta product ... Probably easily shown equivalent ... – mick Aug 06 '16 at 11:27
  • Sorry , i did not know it was duplicate. What happens to duplicates ? Do they get removed ? Can i still see them ? ( I have no exp with this ) – mick Aug 06 '16 at 18:45

0 Answers0