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What is the expression for exact value of pi  using infinite series?
 one year ago
 one year ago
What is the expression for exact value of pi  using infinite series?
 one year ago
 one year ago

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SpacelimbusBest ResponseYou've already chosen the best response.1
Are you allowed to use any series?
 one year ago

SpacelimbusBest 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.
 one year ago

SpacelimbusBest ResponseYou've already chosen the best response.1
but that's only my first intuition and maybe it doesn't answer that problem rigorously
 one year ago

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

SpacelimbusBest 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
 one year ago

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