Summation on HP 42S
09-24-2018, 12:56 AM
Post: #11
 Thomas Klemm Senior Member Posts: 1,773 Joined: Dec 2013
RE: Summation on HP 42S
(09-23-2018 09:25 PM)lrdheat Wrote:  For something a little more complex such as summation 1 through 100 of x^2 - 3*x,

Let us rewrite this expression as:

\begin{align*} x^2 - 3x &= x^2 - x - 2x \\ &= x(x-1) - 2x \\ &= 2\frac{x(x-1)}{2} -2\frac{x}{1} \\ &= 2\binom{x}{2} - 2\binom{x}{1} \end{align*}

$$\sum_{x=1}^{n} 2\binom{x}{2} - 2\binom{x}{1} = 2\binom{n+1}{3} - 2\binom{n+1}{2} = 2\left ( \binom{n+1}{3}-\binom{n+1}{2} \right )$$

This program can be used to calculate the sum:
Code:
00 { 18-Byte Prgm } 01 1 02 + 03 RCL ST X 04 3 05 COMB 06 X<>Y 07 2 08 COMB 09 - 10 2 11 × 12 END

Quote:Produces 323,200 in ~25 seconds

I haven't tested but I assume it's a bit faster than that.

Cheers
Thomas
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 Messages In This Thread Summation on HP 42S - lrdheat - 09-23-2018, 06:14 PM RE: Summation on HP 42S - Didier Lachieze - 09-23-2018, 06:28 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 06:41 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 06:51 PM RE: Summation on HP 42S - ijabbott - 09-23-2018, 07:40 PM RE: Summation on HP 42S - burkhard - 09-25-2018, 12:58 PM RE: Summation on HP 42S - John Keith - 09-25-2018, 04:15 PM RE: Summation on HP 42S - Thomas Klemm - 09-23-2018, 08:29 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 09:25 PM RE: Summation on HP 42S - Didier Lachieze - 09-23-2018, 10:03 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 10:02 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 10:37 PM RE: Summation on HP 42S - Thomas Klemm - 09-24-2018 12:56 AM RE: Summation on HP 42S - Albert Chan - 09-24-2018, 11:56 AM RE: Summation on HP 42S - Thomas Klemm - 09-24-2018, 01:17 AM RE: Summation on HP 42S - Thomas Klemm - 09-24-2018, 01:52 PM RE: Summation on HP 42S - Albert Chan - 09-24-2018, 04:20 PM RE: Summation on HP 42S - pier4r - 09-24-2018, 01:55 PM RE: Summation on HP 42S - Frido Bohn - 09-25-2018, 01:59 PM RE: Summation on HP 42S - Dieter - 09-25-2018, 04:47 PM RE: Summation on HP 42S - Frido Bohn - 09-26-2018, 10:10 AM RE: Summation on HP 42S - Albert Chan - 09-26-2018, 03:13 PM RE: Summation on HP 42S - Albert Chan - 09-25-2018, 05:28 PM RE: Summation on HP 42S - lrdheat - 09-25-2018, 05:17 PM RE: Summation on HP 42S - lrdheat - 09-25-2018, 05:28 PM RE: Summation on HP 42S - Albert Chan - 09-25-2018, 07:17 PM RE: Summation on HP 42S - Valentin Albillo - 09-25-2018, 08:01 PM RE: Summation on HP 42S - Albert Chan - 09-25-2018, 08:59 PM RE: Summation on HP 42S - Gerson W. Barbosa - 09-26-2018, 12:36 PM RE: Summation on HP 42S - Albert Chan - 09-26-2018, 01:23 PM RE: Summation on HP 42S - Gerson W. Barbosa - 09-26-2018, 01:54 PM RE: Summation on HP 42S - pier4r - 09-26-2018, 04:09 PM RE: Summation on HP 42S - Thomas Klemm - 09-27-2018, 03:47 AM RE: Summation on HP 42S - Ángel Martin - 09-27-2018, 05:27 AM RE: Summation on HP 42S - pier4r - 09-27-2018, 10:37 PM RE: Summation on HP 42S - Thomas Okken - 09-28-2018, 12:33 AM RE: Summation on HP 42S - pier4r - 09-28-2018, 01:40 PM RE: Summation on HP 42S - ijabbott - 09-28-2018, 11:20 PM RE: Summation on HP 42S - Albert Chan - 09-29-2018, 12:51 AM RE: Summation on HP 42S - Valentin Albillo - 09-29-2018, 01:15 AM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 01:24 AM RE: Summation on HP 42S - ijabbott - 09-29-2018, 11:58 AM RE: Summation on HP 42S - Albert Chan - 09-29-2018, 12:49 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 01:50 PM RE: Summation on HP 42S - ijabbott - 09-29-2018, 04:06 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 06:15 PM RE: Summation on HP 42S - ijabbott - 09-29-2018, 09:10 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 09:33 PM RE: Summation on HP 42S - Albert Chan - 09-30-2018, 03:03 PM RE: Summation on HP 42S - ijabbott - 09-30-2018, 05:28 PM RE: Summation on HP 42S - brickviking - 10-01-2018, 08:40 AM RE: Summation on HP 42S - pier4r - 09-29-2018, 05:59 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 08:59 PM

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