March 26th, 2019, 10:14 AM  #1 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6  Series
Any idea on these four problems? I have detailed explanations like Derivate this integrate that find C do this do that. ... What I am specifically looking for is a solid example on one of the question to get the idea and do hands on work. Since I didn't do it before, the explanation is too virtual and doesn't make sense to me at this point of learning now. Last edited by skipjack; March 26th, 2019 at 01:03 PM. 
March 26th, 2019, 11:14 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,258 Thanks: 929 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan Last edited by skipjack; March 26th, 2019 at 01:04 PM.  
March 26th, 2019, 12:14 PM  #3 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6 
again as I said these kind of explanations will not make any sense because in the paper I have more detailed explanations. All I need is either detailed step by step recipe or one solid example done step by step. thanks though 
March 26th, 2019, 12:49 PM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,531 Thanks: 1390 
looking at (b) $f(y) = \dfrac{1}{1y}$ $f(0) = 1$ $f^\prime(0) = \left . \dfrac{1}{(1y)^2}\right_{x=0} = 1$ and indeed $f^{(n)}(0) = 1,~\forall n \in \mathbb{N}$ thus the series is $\dfrac{1}{1y} = 1 + y + y^2 + \dots = \sum \limits_{k=0}^\infty y^k$ Now let $y=3x$ $\dfrac{1}{13x} = \sum \limits_{k=0}^\infty (3x)^k$ The series for $\dfrac{1}{14x}$ should be obvious $\dfrac{1}{x+1} = \dfrac{1}{1  (x)} = \sum \limits_{k=0}^\infty (x)^k = \sum \limits_{k=0}^\infty (1)^k x^k$ 
March 26th, 2019, 02:05 PM  #5  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,258 Thanks: 929 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
So what is your value of a? I don't care how complicated your paper is, you need to let us know this. (The default is a = 0 but since I asked would it be so hard to tell me?) Dan  
March 26th, 2019, 05:15 PM  #6 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6 
Romsek thank you so much. you are really very good explainer. and If I did not tell before, you are really a genius in this dumm world. I hope you are making millions using your math knowledge when dumm people are making millions using their nothing.

March 26th, 2019, 06:06 PM  #7 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6 
with your explanation I did b,c,d correctly and fully understanding. but I stuck on a. I did take the derivative of both side after I set it equal to known series and by expanding. I took the derivative of expanded sequence but couldnt see the pattern to convert back to series again. 
March 26th, 2019, 06:18 PM  #8  
Senior Member Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
 
March 26th, 2019, 06:23 PM  #9  
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6  Quote:
 
March 26th, 2019, 06:26 PM  #10 
Senior Member Joined: Apr 2017 From: New York Posts: 155 Thanks: 6 
there are two types of teachers or people with knowledge ( or socalled knowledge) some like Romsek who really knows and really explains. and like you, who is suspicous to have knowledge but definitely no academic capacity to explain anything but critize with assumption. 

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