  # Ramanujan sum of natural numbers - intuitive conundrum!

mathematics Jan 19, 2014

Srinivasa Ramanujan FRS (22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Living in India with no access to the larger mathematical community, which was centred in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he rediscovered known theorems in addition to producing new work

Here’s an amazing mathematical result derived by using Ramanujan summation:

``````1 + 2 + 3 + 4 + 5 + ... = -1/12 (R)
``````

Intuitively, we keep thinking that this must be a really large number (mathematically called a divergent series), right? How can this result be negative number?

Here is a simple way to explain the proof without using any fancy mathematical jargon:

For more such fun with numbers, check Numberphile.com