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Tuesday, January 4, 2011

Infinite series videos

Two videos by Mika Seppala about infinite series:

On the Harmonic Series :


(
In Mathematica I would demonstrate the divergence as follows:
f[n_]:=HarmonicNumber[n,1]
s[n_]:=1+Sum[2^k/2^(k+1),{k,2,Floor[Log[2,n]]}]
t[m_]:=Table[{f[k],s[k]},{k,1,m}]//TableForm//N
)

and about Zeno's Paradox :

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)