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Re: is e < pi ?
Posted:
Jan 11, 2013 1:16 PM


pepstein5@gmail.com wrote in news:901b0e76bb1342e98e752c270fa8fa7c@googlegroups.com:
> On Friday, January 11, 2013 4:10:28 PM UTC, rodp...@gmail.com wrote: >> An obvious answer. But can you prove it ? >> > > 1 + 1 + 1/2! + 1/3! is bounded by 1 + 1 + 1/2 + 1/(2^2) + 1/(2^3) ... > = 3 So e < 3. > > Unlike e, pi is defined differently by different authors. Any > definition should enable the conclusion that pi > 3.
I suppose it's desirable to go from a definition. However:
Since zeta(2) = pi^2/6, we have pi^2 = 6*(1 + 1/4 + 1/9 + ...)
> 6*(1 + int(1/x^2,x=2..infinity)) = 6*(3/2) = 9.
 Cheerfully resisting change since 1959.



