Series

Triangular number

$$k = 1 + 2 + 3 + \cdots + n$$ $$k = \frac{n(n+1)}{2}$$

Squares

$$k = 1^2 + 2^2 + 3^2 + \cdots + n^2$$ $$k = n \frac{(n+1)}{2} \frac{(2n+1)}{3}$$

Harmonic

$$k = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} $$

It's divergent