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Infinite Series Convergence, how?

SOLVED

Re: Infinite Series Convergence, how?

Any idea why the boundary exists or what may cause it?

It is due to divine intervention. See some posts towards the end of this thread.

Re: Infinite Series Convergence, how?

Lou Poulo wrote:

I didn't think that the symbolic processor would calc a numeric result for an infinite sum.

Its capable to do so in some cases - e.g. if we omit the "-0.5" we get Zeta(3/2) (as I posted here in another reply) as result which we could evaluate numerically using float. But for more complex series Mathcads symbolic has to resign.

However, if the float limit is 20 or higher, then the symbolic answer is "undefined," in both versions, leading me to think that "19" did not appear in your evaluation by coincidence. Any idea why the boundary exists or what may cause it?

Not the slightest idea. We discussed exactly that a bit below here http://communities.ptc.com/message/240162#240162

Its also not clear to me why using 0.5 and using the float keyword explicitely yield different results. I always thought that using a single decimal point in a symbolic evaluation has the same effect as using "float, 20" but for some reason beyond me there seems to be a difference.

Ooops, upon rereading my post it just dawnwd on me: decimal point IS float,20. Both would yield undefined.

In my prior post I compared 0.5 to float,10 and of course thats a difference. So one secret is disclosed 😉

Re: Infinite Series Convergence, how?

Trying to use the ratio test or the root test but they both not work.

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