Question

1+2+3+4+.....................=-1/12 how?​

Answer 1

Answer:

The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth partial sum of the series is the triangular number

{\displaystyle \sum _{k=1}^{n}k={\frac {n(n+1)}{2}},}\sum_{k=1}^n k = \frac{n(n+1)}{2},

which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.

Although the series seems at first sight not to have any meaningful value at all, it can be manipulated to yield a number of mathematically interesting results. For example, many summation methods are used in mathematics to assign numerical values even to a divergent series. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of −+

1

/

12

, which is expressed by a famous formula

These methods have applications in other fields such as complex analysis, quantum field theory, and string theory.

In a monograph on moonshine theory, Terry Gannon calls this equation "one of the most remarkable formulae in science".