zbieznosc
: 24 sie 2007, o 16:13
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\(\displaystyle{ \sum_{n=1}^{\infty} \frac{(\arctan(n))^{n}}{2^{n}}}\)
\(\displaystyle{ \sum_{n=1}^{\infty} \frac{(\arctan(n))^{n}}{2^{n}}}\)
kryterium Cauchy'ego:
\(\displaystyle{ \lim\limits_{n\to\infty} \sqrt[n]{\frac{(arctan(n))^{n}}{2^{n}}}=\lim\limits_{n\to\infty} \frac{arctan(n)}{2}=\frac{\pi}{4}}\)
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