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Help me understanding the harmonic analysis

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#1

I am not good in maths and got stuck on harmonic analysis please help me with it.

#2

Hi Rahul,

Happy to help. Could you tell me which part of the analysis are you having trouble with?

#3

Could you please explain how below equation is deduced in harmonic series of K groups
1 + 2 + … + 2^(k - 1) <= N

#4

I also didn’t get this. @Yash_Kumar sir can you please elaborate on this?