know of any more sources to find harmonic divergent induction equations

Please help - very few people even know what Induction is (as we saw at my first attempt to ask this) - I am talking about Mathematical Induction and NOT electrical Induction - I am working on a math project through a Math Institute and it pertains to the Riemann Hypothesis which is considered the most important math question in all of math. Mathematical Induction is considered one of the most important and complex tools in all of math and 1st discussed by people like Plato and Sorites. I have charted 3 Induction equations on a graph. My 3 Induction equations are the Riemann Zeta function, "n(n+1)/2", and "(n2+n)/2". The last 2 equations are literally equal/related but when I charted them I then discovered that all 3 equations are related. I came up with the 2nd equation on my own and then found it at the Summation wiki article and then one day Wikipedia changed the equation on the Summation page to the 3rd equation. My question is ... do you know of any related similar equations? The 2nd and 3rd equations are the same (equal) equation actually but I would like to find at least 1 more please. I read that the Burnoulli numbers are related but I don't think I can break that down like my 3 I have right now. I also found that the Faulhaber's formula may be related and I even saw something called Nicomachus Theorem that may also be related. I am looking for "harmonic" "divergent" infinite series equations. Can you confirm any other of these type of Induction equations I can use? I am basically asking for all the sources of harmonic divergent induction equations so I can at least find one more to add to a chart and basically very few people even know what a harmonic divergent induction equation is and only Wikipedia had a few but I need an expert who may know of a math textbook with more examples.

Answer 1

[glenn farnan]

Wow, I think I can use Nichomachus's Theorem equation! Help me and see if I'm correct in how I reduced it to an easier form:

sumN+Ncubed = (sumN+N)squared

I wonder if this is a case where not having brackets on the left side of the equation makes all the difference from the right side of the equation? *Update - I have found 2 different webpages that write the equation with the squared term on the left of the equation on 1 webpage but then on another webpage the squared term is on the right side of the equation (for those of you wanting to take something from this thread .... my original interest in math had me discover that from the articles on Wikipedia I learned that "Sample Space" equals "Omega(symbol for Sample Space)" equals "SumN" equals the "Summation symbol"!)

Looks good and it is a Number Theory equation and a Squared Triangular equation so it must be a Harmonic Divergent Induction equation.

Do you think that is a fair guess?

Thanks all!!