Disclaimer:

Everything you are about to see when you scroll down is the best of my Mathematical knowledge and a fair bit of imagination. It may, or may not be true. I don’t take any guarantees.

Mathematical Insanity Begins Here!

1 + 2 + 3 + 4 … (to infinity) = -1/12
Now, take that 12 to the other side, or multiply both sides by 12.
We get,
12 + 24 + 36 + 48 …. (to infinity) = -1
Now, take that -1 to the other side, or add 1 on both sides,
We get,
13 [Because,12+1=13] + 24 + 36 + 48 … (to infinity) = 0
Now, make a series of the common difference of the last series,
We get,
0 + 13 + 11 + 12 + 12 ….. (to infinity) = 0
But, why 0 in the right hand side? Well, it is an infinite series right? In an infinite series, you can form any combination of numbers, well I mean, to you have infinite number of 1 (like 1 + 1 +1 + 1 …. etc), you can write it as 1 + 2 + 3 + 4…. or even, 2 + 2 + 2 …. etc, so from the infinite series of 13 + 11 + 12 + 12 ….. you can form, 13 + 24 + 36 + 48…. which has sum 0.
Hence, I put 0 on the right hand side.

Now, we can break that 13 into 12 + 1, so,
12 + 1 + 11 + 12 + 12 …. (to infinity) = 0
Now, add that 1 and 11, we get,12 + 12 + 12 + 12…. (to infinity) = 0

Take 12 as common from the left hand side, and you will have,
12 [1 + 1 + 1 …… (to infinity)] = 0
Send that 12 to the other side, and we will have,
1 + 1 + 1 + 1….. (to infinity) = 0
But then, the above infinite series of 1 can also be written as, 1 + 2 + 3 + 4…..
Now, things get a little crazy, the sum of infinite series of number 1 is 0 while, the sum of infinite series of all the natural numbers is -1/12, so what happened?
Well, I’d say, as we move towards infinity, there’s a boundary or horizon from where on, the laws of mathematics don’t work, just like, the laws of physics don’t work once we’ve reached the event horizon of a black hole.

So, basically, you can consider, black hole to be infinity, and in both cases, the laws of physics or mathematics don’t work once we’ve passed the “event horizon” for both the cases.

Well, that’s all! So, what do you make of it? I don’t know, it may or may not be true, but I’d just call it to be mathematical insanity. If you have any questions, or queries please feel free to drop a comment! 🙂


Abhinav Gyawali

Hello there! I'm a teenager, who spends most of his day thinking and analyzing things. I'm full of ideas and creativity! Hence, I realized a blog would be perfect for me to share my ideas!

Leave a Reply

Your email address will not be published. Required fields are marked *

%d bloggers like this: