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Deathfish
Group Title
What is the expression for exact value of pi  using infinite series?
 2 years ago
 2 years ago
Deathfish Group Title
What is the expression for exact value of pi  using infinite series?
 2 years ago
 2 years ago

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

Deathfish Group TitleBest ResponseYou've already chosen the best response.0
any series will do
 2 years ago

Spacelimbus Group TitleBest ResponseYou've already chosen the best response.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.
 2 years ago

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

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

Spacelimbus Group TitleBest 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
 2 years ago

Neemo Group TitleBest ResponseYou've already chosen the best response.0
\[\sum_{n=0}^{+ \infty }\frac{(1)^n}{2n+1}=\frac{ \pi}{4}\]
 2 years ago
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