Serie convergenta si suma ei

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Cezar Lupu
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Serie convergenta si suma ei

Post by Cezar Lupu »

Sa se arate ca urmatoarea serie este convergenta si apoi sa se gaseasca suma seriei:

\( \sum_{n=1}^{\infty}(-1)^{n}\frac{H_{n}}{n} \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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aleph
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Post by aleph »

O soluţie cu Maple:

> s:=sum(sum(1/n*x^n/k,n=k..infinity),k=1..infinity):
> int( value(diff(s,x)), x=0..-1);
\( -1/12\,{\pi }^{2}+1/2\, \left( \ln \left( 2 \right) \right) ^{2} \)
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