[VA] SRC #012c - Then and Now: Sum

[Valentin Albillo]

  
Hi, all,

A last round of comments before I post my original solution next Sunday night:

John Keith Wrote:Unfortunately my program was just a brute force one and as many have found, brute force is a dead end for this challenge.

Indeed.

John Keith Wrote:After summing 2^17 terms and seeing no convergence, it was obvious that I was getting nowhere.

It would need summing much more terms than that to get just one roughly correct digit.

Quote:I was never anywhere near an analytical solution such as Werner's. Also as you mentioned, the recursion did not turn out to be a problem. It was an interesting and enjoyable challenge, though. Maybe next time...

Glad you liked it. The analytics aren't that difficult at all, it's just getting the correct idea. Thank you very much for your interest and for doing your best to solve it. Maybe next time, though Problems 4, 5 and 6 are allegedly more difficult (though still solvable using an HP-71B) ... or not !

FLISZT Wrote:About the code panels, I will say that it's a pity that you have to scroll as soon as the code is a bit long.

For me, the problem with CODE panels is that when I create a PDF with the thread (which I always do to upload it to my site), the code within them gets truncated and so becomes useless. Thanks for your participation in this thread, Bruno.

Werner Wrote:Apologies for jumping the gun! But I did wait for a full day..

Most commendable. Well, someone had to be first, it might as well be you.

Werner Wrote:Yes, well. The trick I used only works if the sum is convergent to begin with, something I haven't been able to prove.

You can trust me, it is a convergent series and it's not that hard to prove, surely Albert (Chan ?) can provide you with one proof or seven, else I'll obligue.

Werner Wrote:Using the original asymptotic series [...] (thanks^2, Albert!) [...] now, I need the definition only for n<32 instead of 128, and the running time on a real 42S went down to 36 seconds.

Excellent run time indeed, you should've posted "thanks^3" to Albert instead, and when he provides you with the convergence proof you can up it to "thanks^4"  

J-F Garnier Wrote:Now I think I have an idea to calculate the sum in a different (but maybe equivalent) way than Werner, and my understanding is that it will also prove that the sum is convergent.

Good. See ? Perseveration was the key and eventually you did manage, as I said you would.

J-F Garnier Wrote:Edit: Result 2.08637766501 confirmed. I will post my HP-71B program and comments soon...

Perfect. I can confirm that the result is indeed correct to 12 digits. Eagerly waiting for you to post your HP-71B program and comments. You have till next Sunday night.

Werner Wrote:I found another, similar way, but I fear it's the same as J-F's, so I will hold out till he posted his solution ;-)

Most considerate of you, J-F will surely be most pleased.

V.