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Ramanujan Infinite Series: How The Sum 1+2+3+4+... = -1/12?
2023年10月19日 · The series 1+2+3+4+… is a divergent sum because it progressively becomes bigger and bigger until it reaches infinity. If this is so, or at least it logically seems to be, how did Ed Copeland manage to converge it, and even further… to a …
Infinite Series - Numberphile
2019年4月4日 · Fields Medallist Charlie Fefferman talks about some classic infinite series. Charles Fefferman at Princeton: https://www.math.princeton.edu/people/charles-fefferman.
ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12 — Numberphile
2014年1月9日 · The sum of all natural numbers (from 1 to infinity) produces an "astounding" result. Tony Padilla and Ed Copeland are physicists at the University of Nottingham.
I've seen the Numberphile video that shows the infinite set ... - Reddit
2022年3月26日 · There is value in the technique of Ramanujan summation. Ramanujan summation gives us a way to assign values to classically divergent series. It does require a redefinition of infinite summation from the limit of the sequence of partial sums. So, to say this sum is false is not entirely correct.
Why is the sum over all positive integers equal to -1/12?
Recently, sources for mathematical infotainment, for example numberphile, have given some information on the interpretation of divergent series as real numbers, for example $\sum_{i=0}^\infty i = ...
Questions about the Numberphile 'astounding result' that the sum …
2015年3月20日 · The nth partial sum is the sum of the first n terms. This gives you a sequence of numbers, and if it converges to a limit, we say that's the sum of the infinite series. For example, the sum 1+1/2+1/4+1/8.... has the sequence of partial sums 1, 3/2, 7/4, 15/8... and it …
sequences and series - Infinite sum of ones - Mathematics Stack Exchange
Infinite sum of ones. Consider the following infinite series: Rewrite it that way: M = (1) + (1 + 1) + (1 + 1 + 1) + (1 + 1 + 1 + 1) + ... = 1 + 2 + 3 + 4 + ... Given that the sum of integers is proven to equal - 1 12 1 12, I obtain: Which contradicts the initial statement.
ELI5 how the sum of all natural numbers to infinity equals -1/12
2015年3月18日 · As what u/Rikkety linked to, Numberphile covered it very well. The reason it works is because it doesn't use "pure" math. In the video, the show that if you have the infinite sequence: 1-1+1-1+1-1+1-1+..., the sequence goes on forever (hence infinite sequence), but if you were to stop it at random, it will either equal 1 or 0, so they reason ...
Infinity or -1/12? | plus.maths.org
2014年2月18日 · 1+2+3+4+... then the answer to this sum is -1/12. The idea featured in a Numberphile video (see below), which claims to prove the result and also says that it's used all over the place in physics. People found the idea so astounding that it even made it …