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 :