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Calculus 2 help please!

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chapz
Posts: 10182 - Karma: 66
hey guys, so i have to do a lame online assignment. i just need help with one problem...

heres the series
Click for larger image

http://euler.vaniercollege.qc.ca/webwork2_files/tmp/equations/53/98c3c5470b2f5e73a7dd7a1385f7671.png (in case the pic doesnt work)



anyways, i need to know if it converges absolutely, conditionally, or if it diverges.

thanks in advance guys!
May 2 2009 6:19PM
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chapz
Posts: 10182 - Karma: 66
haha the pic is a fail.... i guess png files arent supported. anyways, just go to the link

http://euler.vaniercollege.qc.ca/webwork2_files/tmp/equations/53/98c3c5470b2f5e73a7dd7a1385f7671.png
May 2 2009 6:20PM
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An10a_Eng
Posts: 2505 - Karma: 28
i cant read what the series is but it will converge conditionally if

limit as n goes to infinity of the sequence = 0
it is a  decreasing decreasing sequnce

to test for ablsolute convergence
take the absolute value of hte series and see if that converges. if it does its absolutely if not its not



May 2 2009 6:23PM
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An10a_Eng
Posts: 2505 - Karma: 28
use the ratio test whenever you have factorials
May 2 2009 6:24PM
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steezeandskis
Posts: 646 - Karma: 21
alt series-  un= 1/3^n*n! so 3 things need to be true to converge1- un is always positive- check
2. un>un+1 check and 3. un goes to zero, check so it converges not to determine conditional vs absolute take the abs value of the series and see if that converges.  so if 1/ 3^n*n! converges, which it does, then it will be absolutely convergent. 
May 2 2009 6:25PM
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chapz
Posts: 10182 - Karma: 66
yeahh i know... but im having trouble simplifying the fucker. (3^n)(n factorial) is weird when you have to substitute the n as n+1
May 2 2009 6:26PM
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steezeandskis
Posts: 646 - Karma: 21
this can also work but its easier to use alt series method
May 2 2009 6:26PM
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An10a_Eng
Posts: 2505 - Karma: 28
3^(n+1) = 3*3^n

that usually helps in those types of problems
May 2 2009 6:27PM
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An10a_Eng
Posts: 2505 - Karma: 28
alt test will only prove conditional convergence. gotta use the ratio test to prove absolute
May 2 2009 6:28PM
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An10a_Eng
Posts: 2505 - Karma: 28
also (n+1)! = (n+1)(n!)
May 2 2009 6:29PM
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chapz
Posts: 10182 - Karma: 66
ok so i think i simplified it properly.

i ended up getting 1/3(n+1)

so if i take the limit as n goes to inf, i get 0... so since L is less than one, according to RT, its absolutely convergent?
May 2 2009 6:30PM
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steezeandskis
Posts: 646 - Karma: 21
then you take the abs value of it and solve using geo series?
May 2 2009 6:31PM
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An10a_Eng
Posts: 2505 - Karma: 28
yeah that sounds right
May 2 2009 6:32PM
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An10a_Eng
Posts: 2505 - Karma: 28
you could use any method you want to prove absolute but thatd be wierd to do using geometric series test. with factorials i found it easiest to use the ratio test. if it was just 1/(3^n) id use geometric series
May 2 2009 6:34PM
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An10a_Eng
Posts: 2505 - Karma: 28
this stuff isnt really to fresh in my mind though
May 2 2009 6:34PM
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steezeandskis
Posts: 646 - Karma: 21
true but since 1/n! goes to zero can you ignore it?  i cant remember and i have this final in a week so if you cant that would be very nice to know haha
May 2 2009 6:35PM
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chapz
Posts: 10182 - Karma: 66
ahh YES it was right! thanks a bunch guys.
May 2 2009 6:36PM
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An10a_Eng
Posts: 2505 - Karma: 28
im not 100% sure that you can just ignor stuff. i was never told i could anyway. to be sure id look at the whole denominator.  you could use direct comparison and say that the 1/(n!) converges so for any x >1 the sereis 1/(x*n!) will converge because it is less than 1/(n!). when i took calc 2 doing the ratio test for things like that usually worked the best cuz a ton of shit cancels out.
May 2 2009 6:39PM
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An10a_Eng
Posts: 2505 - Karma: 28
i can give you the link for old calc 2 for engineers finals and answers from CU boulder if you wanna practice
May 2 2009 6:41PM
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steezeandskis
Posts: 646 - Karma: 21
im actually in calc 2 for engineers at boulder now so ive got those tests but thanks bro.  you go to Boulder?
May 2 2009 6:44PM
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An10a_Eng
Posts: 2505 - Karma: 28
haha yeah im gettin ready for the calc 3 final...bright and early on wednesday. who your prof?
May 2 2009 6:45PM
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steezeandskis
Posts: 646 - Karma: 21
I have Dr bhat hes pretty  ill.  Who do you have for calc 3?  and what year are you?
May 2 2009 6:50PM
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An10a_Eng
Posts: 2505 - Karma: 28
im a freshman and i have bhat for 3. im a big fan of him. i had norris for 2 and hes a cool dude too. im a freshman. you
May 2 2009 6:52PM
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An10a_Eng
Posts: 2505 - Karma: 28
i think our finals are at the same time in the same room
May 2 2009 6:52PM
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steezeandskis
Posts: 646 - Karma: 21
mines in muen E050 so if yours is then then yes
May 2 2009 6:59PM
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An10a_Eng
Posts: 2505 - Karma: 28
im in math100 so i guess not. mary nelsons are in the same room from what i hear
May 2 2009 7:00PM
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steezeandskis
Posts: 646 - Karma: 21
ya, who would you suggest for calc 3?
May 2 2009 7:02PM
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An10a_Eng
Posts: 2505 - Karma: 28
Bhat or Norris. as you know, Bhat teaches you like your retarded and know nothing about anything, which is very nice. Norris assumes your smart and can sometimes be a little harder to follow in lecture but i still go to Norris for office hours in calc 3 cuz hes really helpful in a one on one. I never hald mary nelson but the people i know who have had her took her again. I went to one of her reviews and she was in the middle of Bhat and Norris as far as how smart she assumed you are but shes not funny like Bhat or Norris. id go with either bhat or norris, which ever one fits your schedule the best. Dan Larremore is my ta for Calc 3 and he is hte best TA ive had so try to get him
May 2 2009 7:18PM
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