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Math Help - Finding the sum of a Taylor series

  1. #1
    VkL
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    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
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    VkL
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    Quote Originally Posted by VkL View Post
    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?
    .
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