Prime calculator sum(1.0002^n/n, 1, 20000)
12-27-2020, 03:04 AM
Post: #1
 Gil Senior Member Posts: 597 Joined: Oct 2019
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
12-27-2020, 04:16 AM
Post: #2
 Joe Horn Senior Member Posts: 2,002 Joined: Dec 2013
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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<0|ɸ|0>
-Joe-
12-27-2020, 04:27 AM
Post: #3
 toml_12953 Senior Member Posts: 2,097 Joined: Dec 2013
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
Cui bono?
12-27-2020, 10:37 AM
Post: #4
 Gil Senior Member Posts: 597 Joined: Oct 2019
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
12-27-2020, 10:53 AM
Post: #5
 toml_12953 Senior Member Posts: 2,097 Joined: Dec 2013
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
Cui bono?
12-27-2020, 01:46 PM
Post: #6
 Steve Simpkin Senior Member Posts: 1,164 Joined: Dec 2013
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
12-27-2020, 03:17 PM
Post: #7
 Tyann Senior Member Posts: 387 Joined: Oct 2014
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
12-27-2020, 05:32 PM
Post: #8
 Gil Senior Member Posts: 597 Joined: Oct 2019
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
12-27-2020, 05:35 PM
Post: #9
 Gil Senior Member Posts: 597 Joined: Oct 2019
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Sorry, full speed gives 8.9"
on my Galaxy S6 Emu48/HP50G.

Regards,
Gil
12-27-2020, 05:43 PM (This post was last modified: 12-28-2020 02:16 PM by StephenG1CMZ.)
Post: #10
 StephenG1CMZ Senior Member Posts: 1,033 Joined: May 2015
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?

[incorrect formula deleted]
See my later post

Stephen Lewkowicz (G1CMZ)
https://my.numworks.com/python/steveg1cmz
12-27-2020, 05:56 PM
Post: #11
 lrdheat Senior Member Posts: 856 Joined: Feb 2014
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)
12-27-2020, 07:03 PM (This post was last modified: 12-27-2020 07:03 PM by John Keith.)
Post: #12
 John Keith Senior Member Posts: 1,027 Joined: Dec 2013
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.
12-27-2020, 08:07 PM
Post: #13
 lrdheat Senior Member Posts: 856 Joined: Feb 2014
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
12-27-2020, 10:43 PM
Post: #14
 Gerson W. Barbosa Senior Member Posts: 1,580 Joined: Dec 2013
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
CASIO fx-991LAX: 28.1439738342463
15 min < t < 18 min
12-28-2020, 03:20 AM
Post: #15
 Valentin Albillo Senior Member Posts: 1,100 Joined: Feb 2015
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.

All My Articles & other Materials here:  Valentin Albillo's HP Collection

12-28-2020, 10:47 AM
Post: #16
 ijabbott Senior Member Posts: 1,293 Joined: Jul 2015
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
12-28-2020, 12:59 PM
Post: #17
 _nmr_ Junior Member Posts: 14 Joined: Nov 2017
RE: Prime calculator sum(1.0002^n/n, 1, 20000)
Casio fx-5800p:
28.14397383, about 29 minutes.
12-28-2020, 02:03 PM
Post: #18
 StephenG1CMZ Senior Member Posts: 1,033 Joined: May 2015
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)
https://my.numworks.com/python/steveg1cmz
12-28-2020, 03:02 PM
Post: #19
 Joe Horn Senior Member Posts: 2,002 Joined: Dec 2013
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!

<0|ɸ|0>
-Joe-
12-28-2020, 04:21 PM
Post: #20
 Didier Lachieze Senior Member Posts: 1,632 Joined: Dec 2013
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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