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El_Arrow
 one year ago
Help! I need to find a power series representation for the function
El_Arrow
 one year ago
Help! I need to find a power series representation for the function

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El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino @Concentrationalizing @jim_thompson5910

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0this is what i have so far dw:1437181408215:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0dont know if its right or not

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's not correct. You cannot use the geometric series on that since you still have the denominator squared. You would have to eliminate that squared denominator before you go to that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You can ignore the \(x^{2}\) and integrate \(\frac{1}{(17x)^{2}}\)

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so have dw:1437182143406:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0what do i do after that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thats what you got for the power series representation of the antiderivative?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, basically what I'm having you do is: \[\int\limits_{}^{}\frac{ 1 }{ (17x)^{2} }dx = \sum_{n=0}^{\infty}??\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Shouldn't have ln in your answer.

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437182482351:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Right, there ya go. Now of course you need + C, but that won't be an issue with what we are doing. So what is the power series representation of that function?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0would it be dw:1437182579940:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep. I like to separate everything with power series, though, makes it easier to see simplification a lot of the time. So I would have it written like: \[\sum_{n=0}^{\infty}7^{n1}x^{n}\] Okay, so this series is equal to the antiderivative of what we started with. SO we want to go backwards and get back to where we started, which means I need to differentiate my result. You've seen how to differentiate and integrate series?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so this is the power series representation dw:1437182937373:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so we need to find the radius now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, you essentially take the derivative as normal, you worry about the variable terms while constants just stay as is. So kind of informally, the derivative would be something like this: \[\sum_{n=0}^{\infty}7^{n1}\frac{ d }{ dx }(x^{n})\] Where n is a constant. So what's rhe derivative of \(x^{n}\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But one thing we must also do is raise the index from 0 to 1. This is because, as is, letting the first n be 0 would make the series 0, so we fix that by raising the index by one. Thus taking the derivative would give us: \[\sum_{n=1}^{\infty}7^{n1}nx^{n1}\] Now just multiply in the \(x^{2}\)

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0like this dw:1437183623856:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0cause the x^1 and x^2 add each other right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep. Just have to make the index 1 on your series.

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0so using the power series representation how do i determine its radius of convergence?

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.0@dumbcow is the radius 1/7?

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0yes the radius of convergence is 1/7
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