Mathematical paradoxes | Divergent series | Parity (mathematics) | Geometric series | Grandi's series
In mathematics, the infinite series 1 − 1 + 1 − 1 + ⋯, also written is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703. It is a divergent series, meaning that it lacks a sum in the usual sense. On the other hand, its Cesàro sum is 1/2. (Wikipedia).
1-1+1-1+... Grandi series from a complex analysis angle
In this video I talk about switching the limits of an expression that amounts to the Grandi series - a series which is divergent in real and comlex analysis. I'm also ranting a bit on the History of Science and math StackExchange page and other communities.
From playlist Programming
I Just Can't Believe what the Math is Telling Me
The Grandi's Series history is quite famous. The sum 1-1+1-1+1-1 to infinity should clearly diverge with no dispute. However, this 1-1+1-1+1-1 infinite series has a very controversial answer: 1-1+1-1 = 1/2 ?! How could this be? Here's my option on the Grandi's Series answer and a Grandi'
From playlist Series, Series, Series
This is the first half of a lesson, watch the second half here: http://youtu.be/P913qwtXihk
From playlist Mathematical Exploration
Funny Hyderabadi Bralvi Molana.......
From playlist Humor
This Video Will Open Your Mind
Head to https://squarespace.com/brithemathguy to save 10% off your first purchase of a website or domain using code BRITHEMATHGUY The 1-2+3-4+5-6 series is a bit a mathematical wonder. On one hand, this 1-2+3-4+5-6 series diverges. On the other hand, there are some techniques to assign in
From playlist Series, Series, Series
DesmosLIVE: An Exploration of Desmos + Mathalicious
Kate Nowak of Mathalicious explores a few Mathalicious lessons with Desmos
From playlist Desmos LIVE
One minus one plus one minus one - Numberphile
Discussing the brain-bending Grandi's Series and Thomson's Lamp - featuring Dr James Grime. More links & stuff in full description below ↓↓↓ A little bit of extra footage from the very end of this interview at: http://youtu.be/TgGi1ls1X-0 (on Brady's own channel) See our Zeno's Paradox v
From playlist James Grime on Numberphile
The third video in a series about Ramanujan.This one is about Ramanujan Summation. Here's the wikipedia page for further reading: https://en.wikipedia.org/wiki/Ramanujan_summation Euler-Maclaurin Formula https://en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula --------- Here is a
From playlist My Maths Videos
Thoughts on the 1-1+1-1+... Series - A Gentle Discussion About Analytic Continuation
We're going to mess around with some divergent series in this video, namely the Grandi Series, 1-1+1-1+... and the related series 1-2+3-4+... and I'll hopefully convince you that the sums that are associated with these divergent series make some sense when seen through the lens of calculus
From playlist Math
Solving the Basel Problem ... With a Divergent Series!
The Basel problem asks for the sum of the reciprocals of the square numbers, ζ(2), and was famously solved by Euler. In this video, we will find that a simple argument can be given for the solution of the Basel problem using a mysterious divergent series, which upon some simple operations
From playlist Math
Today we examine this amazing, spine-backed Mammal-like Reptile or Synapsid! We will try to answer questions like: Did dimetrodon have fur? How did dimetrodon walk? And what is the deal with dimetrodon's back? Sources: http://www.bioone.org/doi/abs/10.3158/2158-5520-5.1.104 https://en.wik
From playlist Paleontology Videos
The sum of all counting numbers equals WHAT?
This is the second half of a lesson, watch the first half here: http://youtu.be/yudhkUUzAgY This is a well-known and hugely controversial result. The "proof" I've demonstrated is not the only way to show it - there are far more sophisticated and convincing ways to do it - but suffice to s
From playlist Mathematical Exploration