Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Deathfish

  • 2 years ago

What is the expression for exact value of pi - using infinite series?

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

    Are you allowed to use any series?

  2. Deathfish
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    any series will do

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

    then I recommend using the series for tan^(-1)x, because I know that this series approaches for very large x the value pi / 2, so you can just take a multiply (2 times) of that.

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

    but that's only my first intuition and maybe it doesn't answer that problem rigorously

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

    \[ \lim_{x \to \infty} \tan^{-1} x = \frac{\pi}{2} \] \[ \lim_{x \to \infty} 2 \tan^{-1}x = 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1}x^{2n+1}\]

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

    \[ \large \lim_{x \to \infty} 2 \tan^{-1}x =\lim_{x \to \infty}\ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1}x^{2n+1} \] Shouldn't forget to carry out the limit

  7. Neemo
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\sum_{n=0}^{+ \infty }\frac{(-1)^n}{2n+1}=\frac{ \pi}{4}\]

  8. 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.