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*To*: seul-edu@seul.org*Subject*: Re: [seul-edu] [no longer OT] summation of 1/2x*From*: Ray Olszewski <ray@comarre.com>*Date*: Wed, 05 Apr 2000 11:54:54 -0700*Delivery-Date*: Wed, 05 Apr 2000 14:51:48 -0400*Reply-To*: seul-edu@seul.org*Sender*: owner-seul-edu@seul.org

Actually, this gets me thinking again about Brian's original question -- what language is best for doing mathematical demonstrations? I think we all (me included) answered this question with too little thought about the specific needs of mathematics. Whether Brian meant to write 1/n or (1/2)^n, a lot of the languages we suggested will have difficulties computing the series very far out, due to numerical-analysis limitations. Certainly any Basic I've ever actually used will perform poorly (though Ubasic might handle it okay -- I know it handles large integers well, but I don't know about high-precision floats). With 1/n, you get rounding errors very quickly, since 1/3 is an infinite decimal (its binary representation is also infinite, no?). Depending on how a particular language handles rounding and underflow errors, it might or might not demonstrate the unbounded growth that Jan (correctly) asociates with this series. With (1/2)^n, the number of significant (decimal or binary) digits in the fraction increases by 1 with every step in n -- here too, you'll run into rounding problems very fast. Here too, depending on how a language handles rounding and underflow, the series may or may not asymptotically approach 1 or 2 (depending on if n starts as 1 or 0). So ... does anyone know if ANY of the languages we've collectively suggested handles these problems well? I do know that perl has BigInt and BigFloat packages that are said to handle arbitrarily-large precision. I've actually used BigInt, and (except for speed) it works fine with 100+ digit integers. I haven't used BigFloat. At 11:23 AM 4/5/00 -0700, you wrote: ><sigh> Looks like I missed it too, Jan, jm ... I read the problem as the one >I assumed Brian meant (sum of (1/2)^n instead of what he actually wrote (1/n). > >At 01:06 PM 4/5/00 -0500, Jan wrote [in part]: > >>> so you can prove that 1/2+1/4+1/8+..+1/2n+.. = 1 >> >>Actually, that is 1/2^n (one over 2 to the n), not 1/2n. As a matter of >>fact, the series 1/n does not have a finite sum. > ------------------------------------"Never tell me the odds!"--- Ray Olszewski -- Han Solo Palo Alto, CA ray@comarre.com ----------------------------------------------------------------

**Follow-Ups**:**Re: [seul-edu] [no longer OT] summation of 1/2x***From:*Rakis <rakis@wt.net>

**Re: [seul-edu] [no longer OT] summation of 1/2x***From:*LUK ShunTim <cestluk@polyu.edu.hk>

**yacas Re: [seul-edu] [no longer OT] summation of 1/2x***From:*rnd@sampo.karelia.ru

**Re: [seul-edu] [no longer OT] summation of 1/2x***From:*Jan Hlavacek <jhlavacek@sf.edu>

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