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Summation on HP 42S
09-26-2018, 01:54 PM
Post: #30
RE: Summation on HP 42S
(09-26-2018 01:23 PM)Albert Chan Wrote:  
(09-26-2018 12:36 PM)Gerson W. Barbosa Wrote:  ...

'∑(k=1,n,2/(k*(k+3)))'
EVAL
COLLECT

What does it say ? I bet it look complicated ... Big Grin

Indeed it is:

'(11*n^2+48*n+49)*n/(9*((n+3)*((n+2)*(n+1))))'

Well, that’s the price to pay...

(09-26-2018 01:23 PM)Albert Chan Wrote:  Actually, the sum is very easy, once you recognized above formula

∑(k=1,n,2/(k*(k+3)))
= 2/3 * ∑(k=1,n,3/(k*(k+3)))
= 2/3 * ∑(k=1,n, 1/k - 1/(k+3))

If you tried out different values of k, the sum have at most 6 terms. All the rest cancelled out.

∑(k=1,n,2/(k*(k+3))) = 2/3 * (1 + 1/2 + 1/3 - 1/(n+1) - 1/(n+2) - 1/(n+3))


Or

∑(k=1,n,2/(k*(k+3))) = 2/3 * (11/6 - 1/(n+1) - 1/(n+2) - 1/(n+3))

Very nice!
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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 - 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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