Taylor series question(s)

[rir0302]

Since for 1/(1-x) it would be x^n, I thought this would be (-x)^n, but it wasn't correct. Can someone explain the right answer?

I have more questions related to Taylor series, if it's okay I might ask more questions in the thread.

 

[Deleted member 4993]

View attachment 14626

Since for 1/(1-x) it would be x^n, I thought this would be (-x)^n, but it wasn't correct. Can someone explain the right answer?

I have more questions related to Taylor series, if it's okay I might ask more questions in the thread.

Do you know the steps to show the McLaurin series expansion of 1/(1-x) to be x^n?

If you do not remember that, it will be a good idea to look it up in your text-book (or class-notes or internet). It will serve you well.

 

[rir0302]

My textbook just gives it, I found an explanation here: https://socratic.org/questions/how-do-you-find-the-maclaurin-series-for-f-x-1-1-x
and the terms for this are 1−x+x^2−x^3+x^4, etc. I don't understand why it's not something like (-1)^n(x)^n?

 

[Romsek]

\(\displaystyle 1-x+x^2-x^3+x^4 \dots = (-1)^{n}x^n\) exactly as you expect.

 

[rir0302]

Strange, the online grader is saying it's wrong. Here's the format in case I misunderstood something?
[answer here]

Another question though, what does the "index of summation" mean? Another problem wants me to find the "index of summation"th term of a Taylor polynomial.

 

[pka]

Strange, the online grader is saying it's wrong. Here's the format in case I misunderstood something?
View attachment 14649 [answer here]

Another question though, what does the "index of summation" mean? Another problem wants me to find the "index of summation"th term of a Taylor polynomial.

Are you entering \(\displaystyle \sum\limits_{i = o}^n {{{( - 1)}^i}{x^i}} \)
That why I hate online mathematics courses.
I am not at all sure how \(\displaystyle T_n(x)\) is defined in your text material.
The fact is, definitions differ from textbook to textbook. I one taught from a text that changed definitions from one edition to the next,
You might try entering just \(\displaystyle (-1)^ix^i\).

 

[rir0302]

Are you entering \(\displaystyle \sum\limits_{i = o}^n {{{( - 1)}^i}{x^i}} \)
That why I hate online mathematics courses.
I am not at all sure how \(\displaystyle T_n(x)\) is defined in your text material.
The fact is, definitions differ from textbook to textbook. I one taught from a text that changed definitions from one edition to the next,
You might try entering just \(\displaystyle (-1)^ix^i\).

Oh shoot, you were right. My bad for getting the variable wrong. Thanks!