💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 41 Medium Difficulty

Use the power series for $ tan^{-1} x $ to prove the following expression for $ \pi $ as the sum of an infinite series:
$ \pi = 2 \sqrt 3 \sum_{n = 0}^{\infty} \frac {(-1)^n}{(2n + 1) 3^n} $


$$2 \sqrt{3} \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1) 3^{n}}$$


You must be signed in to discuss.

Video Transcript

the problem is, use a power series for tender, the humorous ax to prove of falling expression for pie. Eyes of arm of him in It's serious. First, though, we have attendant thanks. It's true. Some from zero to infinity next to Juan, the part ofthe end halves ax to to us long over to him. Paswan, you absolutely no fax is the last one. Now we like to ACS. Yes, he contused squire into three over three r, one of Bridgette's of three on Behalf Act Hand Wan O Virgin of three. This's the cultural hi over six, and then we use this formula we have. This is also you call two from zero to infinity Nectar wants us apart and house one over two and plus wine halves of three to cover to hand us one. When should we come, too? Want over two three times. Sum from zero between sanity. Next one is a path and Cam's one over two M plus Juan Ham's three inches apart. Then we have pie physical six times, one over duty, three hands. Some come from cereal, twenty men want and Tom's one over to imply us blind house. Great, too notice that six times one over two to three. This's a constitute hamsa root of three. It's a pie. It's equal to two attempts, a route of three times this Siri's.