Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

MathSofiya

  • 2 years ago

\[f(x)=cosh(x)=1+0+\frac{x^2}{2!}+0+\frac{x^4}{4!}+....\] Maclaurin's I'm having some trouble writing this in summation form \[\sum_{n=0}^{\infty} \frac{f^(0)}{n!}x^(n)\] I know that: All even #'s can be written as 2n All odd #'s can be written as 2n+1 \[\sum_{n=0}^{\infty} \frac{...x^{(2n+1)}}{(2n+1)!}\] I think? so how do I write the \[f^n (0)\] correctly?

  • This Question is Closed
  1. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here is my table n f^n x f^n 0 0 coshx 1 1 sinhx 0 2 coshx 1 3 sinhx 0 4 coshx 1

  2. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    these are even values of the exponent, so we use the other formula with the 2n

  3. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ooops

  4. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\sum_{n=0}^{\infty} \frac{...x^{(2n)}}{(2n)!}\]

  5. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    besides that you have written all there is to the series; there is nothing in front of each term that you are missing in your sigma notation

  6. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so just take out the dots lol

  7. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oooh because their just zero's and one's ?

  8. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup try out some values of n plug in n=0 n=1 n=2 etc. you will see you get your series

  9. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    check out my table

  10. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you do not need to represent the 0 terms

  11. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you only need to represent the resulting series

  12. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f(x)=cosh(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+....\] ?

  13. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    your table is for the coefficients, and it should tell you that you are keeping only even exponents, hence you use 2n for the exponent and factorial

  14. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that agrees with your results doesn't it?

  15. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    makes sense

  16. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so there you have it\[\cosh x=\sum_{n=0}^\infty{x^{2n}\over (2n)!}\]a nice, simple series representation

  17. MathSofiya
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[f(x)=cosh(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+....=\sum_{n=0}^{\infty} \frac{x^{(2n)}}{(2n)!}\] final answer. Very good, THankss!

  18. TuringTest
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    welcome!

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.