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KilaTsunami
October, 2024

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For the smart people out there.

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HHB
Posts: 683 - Karma: 14
Im bored doing hw, and i read threads about smart people and calculus. lets see what kinda knowledge we got in the ns forums

so for all you people. ill give you mad karma if you get it right, of course i already know it, i have G status in calc.

just pickin a random problem and random chapter


Series (cant make the symbol for summation so ill use E)

E (2+ (-1)^n)/(n(sqrt(n)) from n=1 to infinity and beyond!!!!!!!111one!!!




yes im a bit of a nerd...
Jan 30 2009 12:46AM
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Alehandro
Posts: 818 - Karma: 12
jesus christ
is that seriously a problem??
Jan 30 2009 12:48AM
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HenniferLopez
Posts: 1319 - Karma: 136
5?
Jan 30 2009 12:49AM
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woolymammoth
Posts: 242 - Karma: 13
let me get back to you in a week, my class is starting series on tuesday
Jan 30 2009 12:50AM
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RudyGarmisch
Posts: 25443 - Karma: 13,844
Get that shit out, I didnt complete college level math courses for more math.
Jan 30 2009 12:50AM
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Elg
Posts: 2998 - Karma: 3,880
I was looking at that problem, and all i noticed was "sqrt" in there. Squirt?
Jan 30 2009 12:51AM
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HHB
Posts: 683 - Karma: 14
ahaha thats square root, not a soda
Jan 30 2009 12:54AM
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zerospinskier
Posts: 4867 - Karma: 350
I haven't taken the series calc in a while, but do you want to know if it converges, or what it converges to?

You could use the alternating series test.
-its monotonic decreasing
-the lim as n goes to infiniti is 0.

So it should converge.

That's all I got. I don't really remember.
Jan 30 2009 1:16AM
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zerospinskier
Posts: 4867 - Karma: 350
Ooooo wait, it's PLUS (-1)^n. Hang on I gotta rethink
Jan 30 2009 1:17AM
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skierdudeguy
Posts: 6574 - Karma: 81
for the record, that doesnt alternate. im not sure if you were trying to make it, but (2+(-1)^n) (or n-1 i dont remember) will either give you 1 or 3... not an alternating series i dont think. but fuck, i got a c in calc 2
Jan 30 2009 1:24AM
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rhcp
Posts: 2598 - Karma: 18
Fuck, I forget how to do this stuff and I just started a math grading job at my university where I grade tests from a calc II class.
Jan 30 2009 1:24AM
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skierdudeguy
Posts: 6574 - Karma: 81
and im pretty sure (that if im right) it doesnt converge
Jan 30 2009 1:25AM
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zerospinskier
Posts: 4867 - Karma: 350
Yeah exactly, that plus sign fucks everything up. I thought it was multiplied at first.
Jan 30 2009 1:26AM
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cclan
Posts: 742 - Karma: 19
to be quite honest something like this doesn't look like it's going to be much use in your everyday life
Jan 30 2009 1:32AM
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HHB
Posts: 683 - Karma: 14
epic. no it doesnt alternate.
im just looking for converge or diverge
pics to show ur work or it didnt happen!!! haha



integral test....
Jan 30 2009 1:43AM
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zerospinskier
Posts: 4867 - Karma: 350
It's just like 1 /  (n)sqrt(n)    which is really easy, but I don't remember how haha.
Jan 30 2009 1:46AM
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lalalalaura
Posts: 6753 - Karma: 68
squirt baby squirt baby squirt
Jan 30 2009 1:47AM
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Static
Posts: 8554 - Karma: 4,089
Click for larger image
Jan 30 2009 1:49AM
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hellomynameisjef
Posts: 5794 - Karma: 167
seven
Jan 30 2009 7:17AM
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HHB
Posts: 683 - Karma: 14

integral test....

Jan 30 2009 10:00AM
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Jwenz
Posts: 8893 - Karma: 7,633
ALright well using the comparison you can just make it 1/n sqrt n which is just n^-3/2

then you integrate from [0, infinity)

Substitute t for infinity

Giving you -2/3t^1/2 + 0

Because the equation with t goes to infinity the series diverges...i think

series was my downfall last semester
Jan 30 2009 10:34AM
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An10a_Eng
Posts: 2505 - Karma: 26
that is correct
Jan 30 2009 12:23PM
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wellpreparedrare
Posts: 651 - Karma: 11
The tops of all equations will either be 1 or 3, seeing that -1 raised to anything above zero will either be -1 or 1; add 2 to either -1 or 1 and you'll get 1 or 3.
The bottom of the equation will be increasing in sequence (from 1 to infiniti) with all equations.
The series will be getting smaller, but always be positive, seeing that eventually 1 or 3 will be divided by infinity-times-its-square-root. 1 or 3 is will be divided into a shitload of little pieces, and the size of one of those pieces is what each equation will equal.
In other words, your equation will eventually reach infiniti, seeing that the series will always be positive and stretches to infiniti.
For all of you that don't know what a series is, all you have to do is add each sum of the equation to the left of the 'E'. Since 'n' is going from 1 to infiniti, you'll get infiniti sums. Hence, the 'series' will be a series of infiniti equation, all in the order from one to infiniti, and each sum being added to the next in the series.
Jan 30 2009 1:53PM
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wellpreparedrare
Posts: 651 - Karma: 11
this only makes sense if you've read the text and gotten the definitions n shit.
Jan 30 2009 1:56PM
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HHB
Posts: 683 - Karma: 14
that is not correct

comparison test shows that

Original integral
Jan 30 2009 2:11PM
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Mac.
Posts: 953 - Karma: 24
We had a problem like that on our AP Challenge today.
Jan 30 2009 3:04PM
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cobra_commander
Posts: 16909 - Karma: 4,687
ya but knowing how to do stuff like that is very useful.

that is if you want to make some money.
Jan 30 2009 3:13PM
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TheQuailman
Posts: 7382 - Karma: 147

I'm only a junior in highschool and I haven't done this yet but...

NUMERATOR

2 + (-1)^n

So sub infiniti for n and your either going to get -1 or 1 depending on whether n is odd or even.  So the numerator is either 1 or 3 (a constant)

DENOMINATOR

n(radical(n))

So sub infiniti for n and it will always increase to infiniti.

So the finale would be..

(1 or 3)/infiniti

which gets closer and closer to zero as infiniti gets larger

So....

Divergent? 

Jan 30 2009 5:13PM
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wellpreparedrare
Posts: 651 - Karma: 11
exactly, but i don't know if divergent is what your teacher wants to see, but that's whatever, the sum is infiniti. if you place 'n' on an x-axis and the sum as n increases along the y-axis, you'll get a graph going up and to the right, which is to positive infiniti.
Jan 31 2009 2:33AM
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Yung_Gnarley
Posts: 9092 - Karma: 3,022
e l e v e n
Jan 31 2009 2:42AM
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.KYLE.
Posts: 1891 - Karma: 59
heres a better question... how could you use that in real life?
Jan 31 2009 2:52AM
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fssnivek
Posts: 283 - Karma: 10
LOL
+10 for that one
does squirt soda still exist?
Jan 31 2009 11:52AM
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