<Dd> 1 + 2 + 3 + 4 + ⋯ = − 1 12, (\ displaystyle 1 + 2 + 3 + 4 + \ cdots = - (\ frac (1) (12)),) </Dd> <P> where the left - hand side has to be interpreted as being the value obtained by using one of the aforementioned summation methods and not as the sum of an infinite series in its usual meaning . </P> <P> In a monograph on moonshine theory, Terry Gannon calls this equation "one of the most remarkable formulae in science". </P> <P> The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc . The nth partial sum is given by a simple formula: </P>

The sum of all natural numbers is 1/12