So, I read this post on the the area of the sine curve some time ago and in the bottom was this equally amazing comment :
I find this extremely beautiful because:
If you still have trouble understanding, follow the blue point in the above gif and hopefully things become clearer.
Have a great day!
Part – I –> Divergence of the Harmonic series
The harmonic series are as follows:
And it has been known since as early as 1350 that this series diverges. Oresme’s proof to it is just so beautiful.
Now replace ever term in the bracket with the lowest term that is present in it. This will give a lower bound on S1.
Clearly the lower bound of S1 diverges and therefore S1 also diverges.
But it interesting to note that of divergence is incredibly small: 10 billion terms in the series only adds up to around 23.6 !