#BoredMathProblemsWithMax
by
_Gill
August 3, 2015 at 3:08 AM UTC
Hey everyone,
Im bored, so I just want to challenge the forums to a math problem thats almost impossible. I saw it on a video, so please don't look it up (unless you're a cheater).
What is the value of 1+2+3+4+5+... (to infinity). The Value of the Sum of Positive Integers.
Hang on, there's a symbol for this... I can't quite remember, but there's literally a symbol that stands for the answer to the question he asking. Not the inifinite symbol, but a different one...
@Max You think that's impossible? You haven't seen some of the problems people can make.
Also, I'm not nice in terms of math problems; I tend to use very difficult ones.
An n by n matrix has entries from the set {1,2,3,...,2n-1}. This is called a flawless matrix if for every k=1,2,3,....,2n-1 the union of the entries in the k-th row and the k-th column of the matrix is {1,2,....,2n-1}.
Prove there are an infinite number of flawless matrices.
Edit 2: Changed the problem, with changed words to make it less searchable. Credits for this problem will come as soon as there is a solution.
I apologize. I forgot the definition of all real numbers from 8th grade xD
A lot of people got the right answer, and even linked the video where I found it from xD, -1/12
To find this value, we need to prove a few things:
1-1+1-1+1-1+1-1+... (going on forever) is equal to 1/2: This is for a number of reasons, but primarily because usually, the value of an infinite serious is equal to the average of its possible answers (at least in this one it is). Therefore (1+0)/2=1/2
Next, we need to prove that 1-2+3-4+5-6+... is equal to 1/4. We find this by adding this infinite series to itself. 1-2+3-4+5-... + 1-2+3-4+... ----------------- 1-1+1-1+1... = 2X (X being the invite series itself). So it then means that 1/2=2X, which is 1/4=X
Now that we have learned all of this, its time to actually solve the series. We will assign the original series (1+2+3+4+...) the variable Y. 1-2+3-4+... will be the variable X (still).
Now, if we take Y-X= 1+2+3+4+5+... -(1-2+3-4+5-...)
This whole thing ends up being Y-X=4+8+12+16+... Factor out the 4: Y-X=4(1+2+3+4+...)
I apologize. I forgot the definition of all real numbers from 8th grade xD
A lot of people got the right answer, and even linked the video where I found it from xD, -1/12
To find this value, we need to prove a few things:
1-1+1-1+1-1+1-1+... (going on forever) is equal to 1/2: This is for a number of reasons, but primarily because usually, the value of an infinite serious is equal to the average of its possible answers (at least in this one it is). Therefore (1+0)/2=1/2
Next, we need to prove that 1-2+3-4+5-6+... is equal to 1/4. We find this by adding this infinite series to itself. 1-2+3-4+5-... + 1-2+3-4+... ----------------- 1-1+1-1+1... = 2X (X being the invite series itself). So it then means that 1/2=2X, which is 1/4=X
Now that we have learned all of this, its time to actually solve the series. We will assign the original series (1+2+3+4+...) the variable Y. 1-2+3-4+... will be the variable X (still).
Now, if we take Y-X= 1+2+3+4+5+... -(1-2+3-4+5-...)
This whole thing ends up being Y-X=4+8+12+16+... Factor out the 4: Y-X=4(1+2+3+4+...)
Since X is equal to 1/4: Y-1/4=4Y
-1/4 = 3Y Y=-1/12
LOL that's the riemann zeta sum, not the euler one. This is just a useful approximation, it actually diverges
Lol I'm still confused. How does it add up to -1/12. I thought a positive+a positive=Positive numbers.
To the number theorist, yes, a positive number+ a positive number is a positive number.
Unfortunately, there's one thing in our way that really prevents us from doing that; the fact that we are dealing with infinite series.
For example, to the number theorist, 1-1+1-1+... is clearly not 1/2, since we could use an argument that Z is a group, so therefore 1-1+1-1+... must be in Z and therefore it's not true that 1-1+1-1+... is 1/2.
To the number theorist, yes, a positive number+ a positive number is a positive number.
Unfortunately, there's one thing in our way that really prevents us from doing that; the fact that we are dealing with infinite series.
For example, to the number theorist, 1-1+1-1+... is clearly not 1/2, since we could use an argument that Z is a group, so therefore 1-1+1-1+... must be in Z and therefore it's not true that 1-1+1-1+... is 1/2.
No it's not just cos it's infinite series but cos it's a Cesaro (i think that's the spelling) sum what equals 1/2, in conventional sense it technically diverges c:
No it's not just cos it's infinite series but cos it's a Cesaro (i think that's the spelling) sum what equals 1/2, in conventional sense it technically diverges c:
Sure, but in number theory, 1+2+3+4+5+.... is clearly not -1/12 due to group theory c:
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