/sci/ - Science & Math

[Anonymous No.6404705]

http://www.youtube.com/watch?v=w-I6XTVZXww

Is /sci/ smart enough to figure out why this is wrong?

[Anonymous No.6404755]

They used the shittiest possible way to prove that (1-1+1-1...) = 1/2.
>hurr durr just take the average
retard.
There is a better way, though, which I believe they covered in a bonus video.
s = 1-1+1-1+1...
1 - s = 1-(1-1+1-1...)
1 - s =1-1+1-1...
1 - s = s
+s +s
2s = 1
/2 /2
s = 1/2

[Anonymous No.6404760]

It's not wrong and stop making these threads

[Anonymous No.6404779]

>>6404755
those types of methods are nice to give some insight into why you get the value, but are actually wrong. correct methods use sums such as Borel, Euler or (specifically nice for this series) Cesàro summations:
<div class="math"> A(x) = \sum_{n=1}^\infty a_nx^n \to \lim_{t\rightarrow\infty} e^{-t}\sum_{n=0}^\infty \frac{t^n}{n!}a_nx^n </div>
<div class="math"> A(x) = \sum_{n=1}^\infty a_n \to \sum_{i=0}^\infty \frac{1}{(1+y)^{i+1}} \sum_{n=0}^i {i \choose n} y^{n+1} a_n .</div>
<div class="math"> A(x) = \sum_{n=1}^\infty a_n \to \lim_{m\to\infty} \frac{1}{m}\sum_{k=1}^m \sum_{n=1}^k a_n </div>

[Anonymous No.6404782]

>>6404760
Technically, -1/12 can be used as the value of that summation.

However, the method displayed in the video is completely wrong, because summations don't work like that.

[Anonymous No.6404794]

>>6404779
>>6404782
Not the OP, but thank you for those suggestions. I thought that result was wrong because I noticed those methods were odd.

[Anonymous No.6404809]

>>6404794
It should be noted that using the '=' symbol for this kind of math is, at best, dishonest, and at worst just false.

They are not equivalent in the same way that 1+1 and 2 are.

[Anonymous No.6404816]

I dropped out of high school and I can't remember simple multiplications at this point.

[Anonymous No.6404826]

>>6404809
"=" isn't defined for those series, so another definition that is the same for the case where = is defined isn't wrong, its just a generalization.

[R !!ISFU7iFCl2G No.6404833]

Physicists can not do math.

[Anonymous No.6404850]

>>6404833
because Abel, euler and borel were phisisists.

[Anonymous No.6404867]

>>6404809
>It should be noted that using the '=' symbol for this kind of math is, at best, dishonest, and at worst just false.
"=" is used in ways like this all the time. e.g. when you write f(n) = O(logn) or arg(z) = pi.

[Anonymous No.6405000]

Because <span class="math">\zeta (-1) = \frac{-1}{12}[/spoiler].
bro do you even Ramanujan Summation and Riemann Zeta Function?

[Anonymous No.6405029]

>>6405000
i.e., it's not wrong. it's correct.

[Anonymous No.6405316]

>>6405029
>>6405000
As state previously in this thread, the answer is correct, but the methods used to find it are bogus.

[Anonymous No.6405378]

>>6404705
>>6404755
If you don't use limits you're going to have a bad time.
The infinite series s=1-1+1-1+1... does not have a defined sum and they should have stopped there.

[Anonymous No.6405818]

ANYONE WHO SEES THIS THREAD:
Look up "Summation of divergent sums", "Riemann Zeta Function Analytic Continuation", and "Ramanujan Summation"
You will learn a little, and you will be less wrong.

this goes for OP as well, and everyone on this thread who says you can't sum divergent series

[Anonymous No.6406866]

Their channel is not to do random equations, it's to demonstrate mathematics and expose interesting ideas to those who otherwise wouldn't encounter them (or at least haven't encountered them yet). They do the same for physics and chemistry.

[Anonymous No.6408258]

>>6405818
>everyone on this thread who says you can't sum divergent series

You can't sum divergant series.

-1/12 is a y intercept of a function defined as the divergent series (1+2+3+4+5+6+7....)

Pic related: See the green line? That represents 1+2+3+4+5+6+7+....

See where the green line intercepts the y axis?

-1/12 isn't a sum, it's a description of a divergent series using a formula that ISN'T classical summation.