Do you know: The summation of 1+2+3—– ∞ is -1/12!

Shocked? I was too. 

We all understand the concept of Infinity. The core principle of infinity is it is endless and cannot be calculated. Thus, it must be impossible to calculate the sum of all numbers to infinity. And the summation of positive numbers must be a positive number again it must be impossible to get a negative result by adding positive numbers. But remarkably the impossible has been achieved by an Indian mathematician Srinivasa Ramanujan, he was also known as “The man who knew infinity”.

Now, let us understand how the value of all of 1+2+3—–∞  is -1/12.

For calculating the value of adding infinitive positive numbers, we must first understand the value of two types of series:

Let,

A = 1-1+1-1+1————– ∞

Now let us subtract both sides by 1:

1-A = 1-1-1+1-1———∞ 1-A = 0+1-1+1-1———-∞ 1-A = 0+A 1 = 2A

A = ½

Now, let:

B = 1-2+3-4——–∞

Now let us subtract both sides by A:

B = 1/4

Now let us find the value of 1+2+3—–∞:

Let,

C = 1+2+3—–∞

Now let us subtract both sides by B:

B-C = (1-2+3-4—–∞) – (1+2+3+4—–∞) B-C = (1-1)+(-2-2)+(3-3)+(-4-4)——— ∞ B-C = 0-4+0-8+0-12———∞ B-C = -4* (1+2+3——–∞) B-C = -4* C B-C = -4C B = -3C C = -B/3

C = -1/12

1+2+3——–∞ = -1/12

Voila!!!!!!!!!!!

This is the magic of mathematics.

So, what can we learn from this value?

• The impossible is possible. No one can imagine calculating the value of Infinity but it has been calculated. So, at some point, you might think your goal is impossible to achieve but at that point remember if infinity can be calculated then nothing is Impossible.
• What we think we know for sure is not always correct. Our general understanding says that the sum of any positive number must be a positive number. But this concept proved that wrong. Likewise in a lot of situations, you might rely on your general understanding which can be quite deceiving. Thus, always keep an open mind about everything.