It can never be equal -1/12, because all the terms you are adding up are positive. Moreover, the sum of the series is divergent, so it cannot converge to a number.
It can never be equal -1/12, because all the terms you are adding up are positive. Moreover, the sum of the series is divergent, so it cannot converge to a number.
This "equality" was first developed by a famous Indian mathematician called Ramanjuan. It arises from something called analytic continuation and the Riemann equation (very advanced mathematics - way over my head).
Of course it doesn't hold in ordinary arithmetic where the normal rules of addition apply. You can read more about it (in an understandable way) here: http://www.qedcat.com/archive/187.html