The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + â‹Ż 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
