MathNet 2026 — Part 06 Question 10

Define a sequence $x_n : n = 1, 2, 3, \dots$ by $x_1 = 1$ and $x_n = x_{n-1} + \sqrt{n}$ for $n \ge 2$. Show that:
$$
\sum_{n=1}^{2018} \frac{1}{x_n} \lt 3.
$$