I have attempted a general pi pattern.
Hope you like it !! Have a nice day!!
Replace 2^n with 2^k.
The RHS will change. However the pattern is not yet established. I don't have a pattern.
Added on March 5, 2022
This expression below gives a relationship to what I have been trying. The result on RHS are in the form of gamma functions and root pi.
I think there is an error.
ReplyDeleteThe numerator must be (2^(n+1))^2 instead of (n+1)^2 as written.
Lemma was a new word till a few years back.
ReplyDeleteLemma is an intermediate theorem.
The above is a Lemma.
So is the earlier one.
Then there is a statement. An infinite series for 1 has to have all the numbers of the universe. This could also be a Lemma.
Some more expressions of mine can be lemmas.
Hey guys!! I had a brief realization of Khinchin constant also.
ReplyDeleteYears back.
Made a blog post too. Need to take a relook.
That leaves 3 more nature blessed constants to realize.
Feigenbaum, Madelung and Chaitin constants.
Sir Andrew Wiles got Abel prize, Copley medal. And he was knighted too.
ReplyDeleteI read that he has written a large book which needs to be read just to understand his proof of Fermat last theorem.
My deepest regards and respect to Sir Andrew Wiles.
ReplyDeleteGood bye folks!!
Would be nice if you explain also no? I can't understand a thing
ReplyDeletePooja Madam, I am not getting it.
ReplyDeleteNo great thing. Just typing out some of the expressions on Wolfram Alpha. So Wolfram Alpha is the big key in all these.
It is about convergence. 1/1+1/2+1/3+. . . . does not converge. But 1/1 squared+ 1/2 squared+ 1/3 squared+. . . . . converges.
I have some intuitions about convergence. Probably have a knack.That's all