It's Grandi's series and its Cesaro sum is 1/2.indeed, IF S EXISTS THEN1/2S = 1 - 1 + 1 -1 + 1 .... (forever)
Find S
S-1 = -1 +1 -1 +1 .... (forever) =-S
so 2S=1
Indeed if S-1 = -S, then S = 1/2. Cauchy and Weierstrass turn in their gravesindeed, IF S EXISTS THEN1/2S = 1 - 1 + 1 -1 + 1 .... (forever)
Find S
S-1 = -1 +1 -1 +1 .... (forever) =-S
so 2S=1
Maybe, but Cauchy would accept it but claim it is not a Cauchy sequence. However,. he might say the Cearo sum does form a Cauchy sequence. And the bespoke sequence does not satisfy the assumptions of the Weierstraß M-test. The Cesaro partial sums form a sequence (1/2, 1/2, 2/3, 2/4, 3/5, 4/7, 4/8,...).Indeed if S-1 = -S, then S = 1/2. Cauchy and Weierstrass turn in their gravesindeed, IF S EXISTS THEN
1/2
S-1 = -1 +1 -1 +1 .... (forever) =-S
so 2S=1![]()
This is an interesting post by Wolfram on that Ramanujan formula: https://blog.stephenwolfram.com/2016/04 ... ramanujan/\(\zeta(-1)=-\frac{1}{12}\)
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I hate those kinds of movies.This is an interesting post by Wolfram on that Ramanujan formula: https://blog.stephenwolfram.com/2016/04 ... ramanujan/\(\zeta(-1)=-\frac{1}{12}\)
बुत् बुद्द सयस
The theory of dynamical systems (Lotka-Voltera model, strange attractors, etc.) and practically all modern theories in economy, sociology or biology would not exist if Cauchy's descendants (Poincaré?) dropped the problem at that point - vide limit sets. (I agree that the S=1/2 makes no sense, though.)the [$]n[$]th-term test for divergence:
If [$]\lim_{n\to\infty}a_{n}\ne 0[$] or if the limit does not exist, then [$]\sum _{n=1}^{\infty }a_{n}[$] diverges
Which is what we've got here
I don't know why but I didn't read the first paragraph about the movie. I started saying what Daniel is speaking about.I hate those kinds of movies.This is an interesting post by Wolfram on that Ramanujan formula: https://blog.stephenwolfram.com/2016/04 ... ramanujan/\(\zeta(-1)=-\frac{1}{12}\)
बुत् बुद्द सयस
As a rule for me, as long as I wrote the paper, I don't watch the movieI don't know why but I didn't read the first paragraph about the movie. I started saying what Daniel is speaking about.I hate those kinds of movies.
This is an interesting post by Wolfram on that Ramanujan formula: https://blog.stephenwolfram.com/2016/04 ... ramanujan/
I understood when I come back to the blog.
As a rule for me, as long as I read a book, I don't watch the movie.
It's just that all these movie are about numbers. I don't understand the fascination. I suppose a movie about [$]\pi[$] is next?I don't know why but I didn't read the first paragraph about the movie. I started saying what Daniel is speaking about.I hate those kinds of movies.
This is an interesting post by Wolfram on that Ramanujan formula: https://blog.stephenwolfram.com/2016/04 ... ramanujan/
I understood when I come back to the blog.
As a rule for me, as long as I read a book, I don't watch the movie.
Pi "The story is about a mathematician and the obsession with mathematical regularity contrasts two seemingly irreconcilable entities: the imperfect, irrational humanity and the rigor and regularity of mathematics, specifically number theory"It's just that all these movie are about numbers. I don't understand the fascination. I suppose a movie about [$]\pi[$] is next?I don't know why but I didn't read the first paragraph about the movie. I started saying what Daniel is speaking about.
I hate those kinds of movies.
I understood when I come back to the blog.
As a rule for me, as long as I read a book, I don't watch the movie.