Mathematics - Limits Question with Solution | TestHub

Let [t] be the greatest integer less than or equal to t. Then the least value of $\mathrm{p}\in \mathbf{N}$ for which ${\lim }_{x\to 0^{+}}\left(x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\dots +\left[\frac{\mathrm{p}}{x}\right]\right)-x^2\left(\left[\frac{1}{x^2}\right]+\left[\frac{2^2}{x^2}\right]+\dots +\left[\frac{9^2}{x^2}\right]\right)\right)\ge 1$ is equal to ________.