Re: A paradoxical series?




On 26/06/2005 17:30, Ann Chance wrote:

> Below is a simple paradox based on a discussion in the excellent book
> "The Road To Reality" by Sir Roger Penrose:
>
> Consider the fact that 1+x^2+x^4+x^6+... = (1-x^2)^(-1)
>
> Putting 2 into this series gives us:
>
> 1+2^2+2^4+2^6+... = (1-2^2)^(-1) = -1/3
>
> While the LHS is obviously positive, the RHS is negative. How is that
> possible?
>

Simply because your series converges only for |x| < 1 (and maybe some |x|=1,
but it's more difficult to study than the simple "D'Alembert criterium")).

.

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