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Topic: Maiximum value of x that maintain the convergence of a series:
Replies: 7   Last Post: Oct 31, 2013 1:10 PM

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 Luis A. Rodriguez Posts: 748 Registered: 12/13/04
Re: Maiximum value of x that maintain the convergence of a series:
Posted: Oct 31, 2013 1:10 PM

El martes, 29 de octubre de 2013 11:15:50 UTC-4:30, Ludovicus escribió:
> Consider the series:
>
> x + x^2 + (x + x^2)^3 + ....
>
> U(n+1) = Un + (Un)^n
>
> Which is the maximum x than maintain the convergence?
>
> I think , 0.3105 < x < 0.311.
>
> Please calculate x and U(100) with 6 correct digits.
>
> Ludovicus

The Ben Bacarise's answer for x1 is correct (Also that the limit is 1). Thanks
Now we have a new mathematical constant with a precision of 34 digits!!

Date Subject Author
10/29/13 Luis A. Rodriguez
10/29/13 James Waldby
10/29/13 Virgil
10/30/13 David C. Ullrich
10/30/13 Virgil
10/30/13 Peter Percival
10/30/13 Peter Percival
10/31/13 Luis A. Rodriguez