# Thread: Finding the sum of a Taylor series

1. ## Finding the sum of a Taylor series

Hello everyone, I have 2 questions to ask that are probebly very simple to all of you. But I Do not understand them. Any help would be appreciated at all! Thanks in advance.

Question 1:

How do you find the exact sum of a Taylor series?

For example,

If that is recognized as a Taylor series, How would the finite sum be calculated?

I am thinking of doing some tests, like ratio test. But that only tell you the convergence / divergence. If this was a finite or infinite geometric series, calculating the sum would be very simple. I don't know how to start here, Thank you.

Question 2:
How would you solve for the EXACT value of x in a Taylor series?

For example,

-x^2 - ((x^3)/2) -((x^4)/3)-((x^5)/4)..... = [x ^ (n+1)] / n = x/3

2. =(

3. Originally Posted by VkL
Hello everyone, I have 2 questions to ask that are probebly very simple to all of you. But I Do not understand them. Any help would be appreciated at all! Thanks in advance.

Question 1:

How do you find the exact sum of a Taylor series?

For example,

hint ... $\textcolor{red}{e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + ...}$

what if x = 4?

Question 2:
How would you solve for the EXACT value of x in a Taylor series?

For example,

-x^2 - ((x^3)/2) -((x^4)/3)-((x^5)/4)..... = [x ^ (n+1)] / n = x/3

huh?
.