Summation of Consecutive Integers

All negative integers from -13 to -1 cancels out all positive integers from 13 to 1. Thus, only 14 is left!

The numbers from -13 to -1 cancels out with the positive integers from 1 to 13. Hence only 14 remains.

As a number's positive and negative summation is 0. So, from -13 to +13 numbers summation is 0. That why, the 14 is only number that is no negative.

So answer is 14

$-13, -12, ....14$

$a_1=-13;d=-12-(-13)=1$

$a_n=a_1+(n-1)d$ $\implies$ $14=-13+(n-1)1$ $\implies$ $27=n-1$ $\implies$ $28=n$

$s=\dfrac{n}{2}(a_1+a_n)=\dfrac{28}{2}(-13+14)=$ $\boxed{14}$

Sn = 28(-13+14)/2 = 14