OT: can somebody help me with this series/sum Calculus II type problem?

[ryan roopnarine]

evening/morning gentlemen, i have a really dumb question i need to ask, and I know that someone here can answer it. first, let me start off by saying that I KNOW i should know how to do this, but it has been a really long time since i've done it, and i'm at my wits end. i'm trying to figure out how to do partial sums in a calculator. every time i attempt to do it this way, they come out wrong, and i don't understand where i'm screwing it up. i've attached an example below. lets say i try to find the s15 of the series/sum, as they've done below. i'm failing in getting my calculator to generate the same number. i really hate to have to ask this this way, but could somebody PLEASE tell me the keystrokes i'd need to punch in to get the s15 number? i've been through the three calculus books i have in my "home library" and i can't see where my fundamental misunderstanding is in doing this. the computer using 2 or 3 math programs comes back with teh same 1.58...answer, so i know it isn't wrong. i'm really not trying to have anyone else do my work for me, its just that i'm at an impass. if somebody could help me, i'd be really be appreciative.

ps...i know this is really lame, but if you all are somewhat receptive, i might ask one or two more things later. thanks.



arrrgh, stupid @## vb won't let me even post gifs as it tries to interpret them as equations
if my typed in equation isn't neat enough, the source is available here, (http://tutorial.math.lamar.edu/AllBrowsers/2414/EstimatingSeries_files/eq0022M.gif) 1/2 way down the page, directly under the fluorescent blue box, marked "example 1"



the series is

(infinity)
____
\
\
\ 1 /n^2
/
/
____

n=1

the actual value is 1.64493....

using n=15 to estimate, or s15, the value comes out to be 1.58044.....

[Anton CH.]

Try to use a higher number of iterations (n=1 to n=200 you get closer to the actual value). At n=15 I get the same 1.5.... on my TI89.

[ryan roopnarine]

Try to use a higher number of iterations (n=1 to n=200 you get closer to the actual value). At n=15 I get the same 1.5.... on my TI89.

is that with you putting the calculator into sequence mode and asking it to manually generate a table or find n=15?

[Anton CH.]

What calculator are you using?

[ryan roopnarine]

What calculator are you using?

ti-83

[ryan roopnarine]

i really suspect that something is wrong with my calculator, so if you could get a little (short bus) with me, i'd really be grateful.

[jgardia]

(Pi)^2/6

[stilljester]

Post it over here CR4 (http://cr4.globalspec.com/) The site has a good equation editor and I'm sure someone will respond.

[Rus]

I'm using TI-83Plus and I get 1.580440283 for the 15th term sum estimate. The 1.64493 that you mentioned as being correct is not possible at the 15th term summation. This sequence converges to a value of 0, but this happens at values much higher than 15. At the 100th summation term the value of 1/n^2 is .0001 and the sum is 1.6349. At the 15th summation the value of 1/n^2 is still high at .00391 and the sum is a poor estimate. So in summary, there is nothing wrong with your calculator, its just that you will never get a closer approximation at the 15th term of the sequence. If you want to know the exact sum, you'll need to plug in a very high number for n and it will effectively give you the sum.

Its finals season huh? :) Gotta love it. HTH

P.S.: I used this site: http://www.stetson.edu/~mhale/teach/ti83.htm#sequences to plug things into my TI. Wish I knew it could do it for me when I was taking Calc II. Then again, that probably wouldn't have taught me to use this stuff and I'd be SOL in Thermodynamics and Transport Phenomenon classes (ChemE woot!) :)

[ryan roopnarine]

um, ok.
for some reason, situationally, it seems, you either have to feed this calculator the wrong number of parenthesis, or the right number, to get it to work. i just finally got it to spit out the 1.58 number by inputting the series with the wrong number of parenthesis. this will be the second TI graphing calculator that i've bought since 1998 (in which) the logic has gone bad, and the calculator has begun to spit out incorrect responses. i'd go buy another one if i weren't so pissed off.

the series, for some reason, needs to be inputted sum(seq(1/x^2, x, 1, 15, 1 for it to work

arrrgh
thankfully, this isn't "really" for one of my classes, but i had to get somebody to confirm that this calculator doesn't work. the 1.6 or pi number isn't from teh calculator, it is the comparison value.

thanks to everybody that posted in this thread.

[Rus]

Following your example I put in sum(seq(1/(x^2), x, 1, 15, 1) and got 1.580440283 I've never come across a TI calc that went loopy like that. Maybe reset it and update the OS? Mine has been with me for about 6 years and has given me no problems.

P.S.: Note that I enclosed the x^2 in parenthesis. I've found that oftentimes that is necessary to do.

[ryan roopnarine]

Following your example I put in sum(seq(1/(x^2), x, 1, 15, 1) and got 1.580440283 I've never come across a TI calc that went loopy like that. Maybe reset it and update the OS? Mine has been with me for about 6 years and has given me no problems.

no, leave the parenthesis off the back of (x^2, and no parenthesis to close the expression, and it works for some reason. i had the same ti83 between 1998 and 2006, and it began to go flaky in the beginniing of 2005. it would take 5 minutes to graph simple things like x^2, and the "processing" bars at the top right of the screen would constantly chug. finally, one day, it said "system ram failure" and never started up again. i know of at least 2 other people that have dying units. i don't know what to do about this thing...i just changed majors, but i might still need to follow along to ti-83/84 instructions or such. hell of a racket they have, really.

[Rus]

no, leave the parenthesis off the back of (x^2, and no parenthesis to close the expression, and it works for some reason. i had the same ti83 between 1998 and 2006, and it began to go flaky in the beginniing of 2005. it would take 5 minutes to graph simple things like x^2, and the "processing" bars at the top right of the screen would constantly chug. finally, one day, it said "system ram failure" and never started up again. i know of at least 2 other people that have dying units. i don't know what to do about this thing...i just changed majors, but i might still need to follow along to ti-83/84 instructions or such. hell of a racket they have, really.

Hmm, mine works your way too. Those TI-89 calcs look mighty tasty for a replacement :) Like I said, you can try resetting all memory and updating the software using another calculator. Maybe it'll help?

[jgardia]

you don't need the parenthesis, because 1/x^2 == 1/(x^2) == (1/x)^2





Following your example I put in sum(seq(1/(x^2), x, 1, 15, 1) and got 1.580440283 I've never come across a TI calc that went loopy like that. Maybe reset it and update the OS? Mine has been with me for about 6 years and has given me no problems.

P.S.: Note that I enclosed the x^2 in parenthesis. I've found that oftentimes that is necessary to do.