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Prime calculator sum(1.0002^n/n, 1, 20000)
12-27-2020, 03:04 AM
Post: #1
Prime calculator sum(1.0002^n/n, 1, 20000)
How to calculate
sum(1.0002^n/n, 1, 20000)
with the build-in template sigma?

To get an approximate answer,
I have to calculate
sum(1.0002^n/n, 1, 10000) + sum(1.0002^n/n, 10001,20000) = 10.9246.

Somewhat cumbersome.

On the HP50G, I get the wished answer by writing
directly sum(1.0002^n/n, 1, 20000).

Thanks for your help.

Regards,
Gil
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12-27-2020, 04:16 AM
Post: #2
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
It works directly in Home, summing 1.0002^X/X from 1 to 20000. Summations in Home apparently do not have the same restriction as CAS. BTW, I think that the correct result is approximately 28.1439738, not 10.9246.


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12-27-2020, 04:27 AM
Post: #3
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-27-2020 03:04 AM)Gil Wrote:  How to calculate
sum(1.0002^n/n, 1, 20000)
with the build-in template sigma?

To get an approximate answer,
I have to calculate
sum(1.0002^n/n, 1, 10000) + sum(1.0002^n/n, 10001,20000) = 10.9246.

Somewhat cumbersome.

On the HP50G, I get the wished answer by writing
directly sum(1.0002^n/n, 1, 20000).

Thanks for your help.

Regards,
Gil

In BASIC I get 28.14397384

Tom L
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12-27-2020, 10:37 AM
Post: #4
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
You are right, I forgot one zero.

A pity anyway to have to switch to HOME to get a simple result.

Observation
To be able to enter the beginning value for n (under the sigma-summation-sign) and the last summation value of n, I had to select TEXTBOOKS notation.

Is it possible to write it "normally" in ALGEBRAIC mode
(or in RPN like in the equation writer of the HP50G)?

Regards,
Gil
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12-27-2020, 10:53 AM
Post: #5
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-27-2020 10:37 AM)Gil Wrote:  You are right, I forgot one zero.

A pity anyway to have to switch to HOME to get a simple result.

Observation
To be able to enter the beginning value for n (under the sigma-summation-sign) and the last summation value of n, I had to select TEXTBOOKS notation.

Is it possible to write it "normally" in ALGEBRAIC mode
(or in RPN like in the equation writer of the HP50G)?

Regards,
Gil

the CAS sum() function is the discrete sum, related to an integral, not an algebraic sum. Are they the same? I'm not a mathematician, so someone else will have to answer.

Tom L
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12-27-2020, 01:46 PM
Post: #6
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
By the way, how long did this summation take to run on the Prime?
G1 vs G2?

I noted the following calculation times (in minutes:seconds) on some of the calculators I tried it on.

Casio fx-CG50
1:13

TI-89
10:40

TI-92
18:55
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12-27-2020, 03:17 PM
Post: #7
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-27-2020 01:46 PM)Steve Simpkin Wrote:  By the way, how long did this summation take to run on the Prime?
G1 vs G2?

I noted the following calculation times (in minutes:seconds) on some of the calculators I tried it on.

Casio fx-CG50
1:13

TI-89
10:40

TI-92
18:55

Hello
G1: 1,7 sec
G2: 0,7 sec

Sorry for my english
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12-27-2020, 05:32 PM
Post: #8
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Just for your information

Summation from 1 to 20 000
of '1.00002^n/n'

gives on my phone Samsung Galaxy S6
with emulated calculator HP50G
with the EMU48 application:

4'12" (calculator "emulated" / original speed)
and 10.9" (full speed).

Regards,
Gil
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12-27-2020, 05:35 PM
Post: #9
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Sorry, full speed gives 8.9"
on my Galaxy S6 Emu48/HP50G.

Regards,
Gil
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12-27-2020, 05:43 PM (This post was last modified: 12-28-2020 02:16 PM by StephenG1CMZ.)
Post: #10
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Perhaps the 10 000 limit is related to the size of lists, which are limited to 10 000 items on the HP Prime?

How about
[incorrect formula deleted]
See my later post

Stephen Lewkowicz (G1CMZ)
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12-27-2020, 05:56 PM
Post: #11
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
HP Prime G2: <0:01
TI NSpire 2 (no CAS): 0:09
CASIO fx-CG50: 1:14
CASSIO CLASSPAD (fx-CP400): 6:49
CASSIO fx-991EX: 17:38

The TI Nspire was a bit high beginning with 9th decimal (28.143973835105)
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12-27-2020, 07:03 PM (This post was last modified: 12-27-2020 07:03 PM by John Keith.)
Post: #12
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-27-2020 03:04 AM)Gil Wrote:  On the HP50G, I get the wished answer by writing
directly sum(1.0002^n/n, 1, 20000).

For the HP 50, the correct syntax is '\GS(n=1, 20000, 1.0002^n/n)' where \GS is the Sigma character (right-shift S).

On a physical HP 50g, I get 28.1439738407 in 354.6 seconds, or just under 6 min.
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12-27-2020, 08:07 PM
Post: #13
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Similar for me on HP 50g using evaluate the term from the equation writer.

CASSIO fx-115ES Plus: 1:26:29

TI-36X Pro: 1:28:52
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12-27-2020, 10:43 PM
Post: #14
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
CASIO fx-991LAX: 28.1439738342463
15 min < t < 18 min
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12-28-2020, 03:20 AM
Post: #15
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-27-2020 10:43 PM)Gerson W. Barbosa Wrote:  CASIO fx-991LAX: 28.1439738342463
15 min < t < 18 min

Thomas Okken's awesome Free42 Decimal for Android on a Samsung Galaxy tablet:

         LBL "SUMA"
         20000
         0
         LBL 00
         1.0002
         RCL ST Z
         Y^X
         RCL/ ST L
         +
         DSE ST Y
         GTO 00


[R/S] ->    28.14397383505516924725756564071173    in 2.46 sec.

V.

  
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12-28-2020, 10:47 AM
Post: #16
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-27-2020 05:56 PM)lrdheat Wrote:  CASSIO fx-991EX: 17:38

(12-27-2020 08:07 PM)lrdheat Wrote:  CASSIO fx-115ES Plus: 1:26:29

TI-36X Pro: 1:28:52

For comparison with the above:

TI-30X Pro MathPrint: 20:09 answer: 28.14397384 (28.14397383500)

Slower than its rival Casio fx-991EX on this task.

— Ian Abbott
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12-28-2020, 12:59 PM
Post: #17
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Casio fx-5800p:
28.14397383, about 29 minutes.
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12-28-2020, 02:03 PM
Post: #18
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
If you wanted one sum rather than two (1-10000 plus 10001-20000) you could use

Sum(1.0002^n/n + 1.0002^(10000+n)/(10000+n),n,1,20000/2)

Which only has 10 000 terms.
But it is no faster than the other expression.
(the formula I tried earlier was incorrect)

Stephen Lewkowicz (G1CMZ)
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12-28-2020, 03:02 PM
Post: #19
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-28-2020 03:20 AM)Valentin Albillo Wrote:  Thomas Okken's awesome Free42 Decimal for Android on a Samsung Galaxy tablet:

         LBL "SUMA"
         20000
         0
         LBL 00
         1.0002
         RCL ST Z
         Y^X
         RCL/ ST L
         +
         DSE ST Y
         GTO 00


[R/S] ->    28.14397383505516924725756564071173    in 2.46 sec.

Thanks, Valentin! Although I get similar timing with Free42 on my laptop computer, my DM42 takes forever, apparently updating the stack display constantly even though the program contains no display commands. Anybody know how to tell the DM42 not to update the stack display while running? Thanks in advance!

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12-28-2020, 04:21 PM
Post: #20
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
(12-28-2020 03:02 PM)Joe Horn Wrote:  Anybody know how to tell the DM42 not to update the stack display while running? Thanks in advance!

You can try with RefLCD set to 0.
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