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#### DeusAbscondus

##### Active member

- Jun 30, 2012

- 176

Does one assess $x$ at $x=0$ for the entire series? (If so, wouldn't that have the effect of "zeroing" all the co-efficients when one computes?)

only raising the value of $k$ by $1$ at each iteration?

and thereby raising the order of derivative at each iteration?

$$\sum_{k=0}^{\infty}\frac{f^{k}(0)}{k!} x^k= f(0)+\frac{df}{dx}|_0 \ x + \frac{1}{2!}\frac{d^2f}{dx^2}|_0 \ x^2+ \frac{1}{3!}\frac{d^3f}{dx^3}|_0 \ x^3+ ....$$

I have no experience with series or sequences, so, I

In the interim, however, I am currently enrolled in a Math course that looks at Calculus by

I am an adult beginner at Math, having done an introductory crash course in Calculus last year; I wanted to flesh this out: hence my current enrolment.

But I am at a loss to know how to manipulate the notation above and would appreciate a worked solution for some simple $f(x)$ (I won't nominate one, so as to preclude the possibility of my cheating on some set work)

I just need to see this baby in action with a "well-behaved function" of someone else's choosing, with some notes attached if that someone would be so kind.

Thanks,

Deo Abscondo

only raising the value of $k$ by $1$ at each iteration?

and thereby raising the order of derivative at each iteration?

$$\sum_{k=0}^{\infty}\frac{f^{k}(0)}{k!} x^k= f(0)+\frac{df}{dx}|_0 \ x + \frac{1}{2!}\frac{d^2f}{dx^2}|_0 \ x^2+ \frac{1}{3!}\frac{d^3f}{dx^3}|_0 \ x^3+ ....$$

I have no experience with series or sequences, so, I

*know*I have to remedy this gap in my knowledge.In the interim, however, I am currently enrolled in a Math course that looks at Calculus by

*beginning*with Taylor series.I am an adult beginner at Math, having done an introductory crash course in Calculus last year; I wanted to flesh this out: hence my current enrolment.

But I am at a loss to know how to manipulate the notation above and would appreciate a worked solution for some simple $f(x)$ (I won't nominate one, so as to preclude the possibility of my cheating on some set work)

I just need to see this baby in action with a "well-behaved function" of someone else's choosing, with some notes attached if that someone would be so kind.

Thanks,

Deo Abscondo

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