Thanks for investigating. I tried to use sympy this way:
sum(log(1-2^-k),k,1,oo,algorithm="sympy")
but this failed for other reasons (NotImplementedError: conversion to
SageMath is not implemented)
wdjo...@gmail.com schrieb am Dienstag, 10. Dezember 2024 um 14:58:49 UTC+1:
> On Tue, Dec 10, 2024 at 8:43 AM 'OHappyDay' via sage-support <
> sage-s...@googlegroups.com> wrote:
>
>> I tried to evaluate the infinite product:
>>
>> prod((2^n-1)/2^n) (n=1,oo)
>>
>> by converting the product to a sum via logarithm:
>>
>> sum(log(1-2^-k),k,1,oo)
>>
>> The sum (and thus the product) should, according to WolframAlpha,
>> converge with a final value of about
>>
>> -1.24206
>>
>
> Sympy does it:
>
> sage: *from* *sympy* *import* oo, Sum, log, Product
>
> sage: p0 = Product((1-1/2^n), (n, 1, oo))
>
> sage: p0.evalf()
>
> 0.288788095086602
>
> sage: s0 = Sum( log(1-1/2^n), (n, 1, oo))
>
> sage: s0.evalf()
>
> -1.24206209481242
>
> sage: exp(-1.242) ## check
> 0.288806027885956
>
>
>>
>> This video (https://www.youtube.com/watch?v=KDyHJlNkov8) indicates that
>> the product converges with an irrational value.
>>
>> Sage reports that the sum is divergent.
>>
>> Ideas? Is this again a failure in Maxima?
>>
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