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March 26th, 2019, 10:14 AM   #1
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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.
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March 26th, 2019, 11:14 AM   #2
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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.
When the problem says "compute the series" what value of x are we computing about? x = 0? (Clearly not x = 1!)

-Dan

Last edited by skipjack; March 26th, 2019 at 01:04 PM.
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March 26th, 2019, 12:14 PM   #3
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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
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March 26th, 2019, 12:49 PM   #4
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looking at (b)

$f(y) = \dfrac{1}{1-y}$

$f(0) = 1$

$f^\prime(0) = \left . \dfrac{1}{(1-y)^2}\right|_{x=0} = 1$

and indeed

$f^{(n)}(0) = 1,~\forall n \in \mathbb{N}$

thus the series is

$\dfrac{1}{1-y} = 1 + y + y^2 + \dots = \sum \limits_{k=0}^\infty y^k$

Now let $y=3x$

$\dfrac{1}{1-3x} = \sum \limits_{k=0}^\infty (3x)^k$

The series for $\dfrac{1}{1-4x}$ should be obvious

$\dfrac{1}{x+1} = \dfrac{1}{1 - (-x)} =
\sum \limits_{k=0}^\infty (-x)^k =
\sum \limits_{k=0}^\infty (-1)^k x^k$
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March 26th, 2019, 02:05 PM   #5
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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
The "usual" way to come up with a power series is by use of a Taylor series. Refering to the defining equation (the first equation listed on the site) we see we need a value of "a" to compute the derivatives. romsek's example uses a = 0 but other values of a can be used.

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
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March 26th, 2019, 05:15 PM   #6
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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.
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March 26th, 2019, 06:06 PM   #7
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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.

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March 26th, 2019, 06:18 PM   #8
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Quote:
Originally Posted by Leonardox View Post
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.

This is what happens when you don't put any effort into your homework and just have someone spoon feed it to you. These kinds of questions are usually meant to make you spend a bit of time thinking about what a Taylor series is. It's not surprising you actually haven't learned anything except how to do the exact example Romsek showed you.
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March 26th, 2019, 06:23 PM   #9
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Originally Posted by SDK View Post
This is what happens when you don't put any effort into your homework and just have someone spoon feed it to you. These kinds of questions are usually meant to make you spend a bit of time thinking about what a Taylor series is. It's not surprising you actually haven't learned anything except how to do the exact example Romsek showed you.
I finished all understanding perfectly. the rest of the world that is exactly what I was meaning thanks for solid example.
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March 26th, 2019, 06:26 PM   #10
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there are two types of teachers or people with knowledge ( or so-called 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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