On Tue, Dec 10, 2024 at 8:43 AM 'OHappyDay' via sage-support < sage-support@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? > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion visit > https://groups.google.com/d/msgid/sage-support/fc804b35-7d19-4677-a793-a0c1c76d8391n%40googlegroups.com > <https://groups.google.com/d/msgid/sage-support/fc804b35-7d19-4677-a793-a0c1c76d8391n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/sage-support/CAEQuuAV7uVTG_Z4oST5KgK%3D%3DiAM%2B%2BtJvE7u7DCvraXrmKRBRKA%40mail.gmail.com.
