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Topic: is e < pi ?
Replies: 4   Last Post: Mar 9, 2013 8:18 AM

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Bart Goddard

Posts: 1,485
Registered: 12/6/04
Re: is e < pi ?
Posted: Jan 11, 2013 1:16 PM
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pepstein5@gmail.com wrote in
news:901b0e76-bb13-42e9-8e75-2c270fa8fa7c@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.




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