A community for students.
Here's the question you clicked on:
 0 viewing
Deathfish
 3 years ago
What is the expression for exact value of pi  using infinite series?
Deathfish
 3 years ago
What is the expression for exact value of pi  using infinite series?

This Question is Closed

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.1Are you allowed to use any series?

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.1then 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.

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.1but that's only my first intuition and maybe it doesn't answer that problem rigorously

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.1\[ \lim_{x \to \infty} \tan^{1} x = \frac{\pi}{2} \] \[ \lim_{x \to \infty} 2 \tan^{1}x = 2 \sum_{n=1}^\infty \frac{(1)^{n+1}}{2n1}x^{2n+1}\]

Spacelimbus
 3 years ago
Best ResponseYou've already chosen the best response.1\[ \large \lim_{x \to \infty} 2 \tan^{1}x =\lim_{x \to \infty}\ 2 \sum_{n=1}^\infty \frac{(1)^{n+1}}{2n1}x^{2n+1} \] Shouldn't forget to carry out the limit

Neemo
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sum_{n=0}^{+ \infty }\frac{(1)^n}{2n+1}=\frac{ \pi}{4}\]
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.