Let f(x) be a non-negative, continuous, decreasing function defined for x ≥ N, where N is an integer. Then, the series ${\sum }_{n=N}^{\infty }f\left(n\right)$ converges if and only if the integral ${\int }_N^{\infty }f\left(x\right)\text{d}x$ converges. For example, setting N = 1 and f(x) = 1/x shows that the harmonic series diverges as ${\int }_1^X\frac{\text{d}x}{x}=\text{ln}X$ tends to infinity as X tends to infinity.