Question 57
$x$ is a positive real number if $[x]$ denotes the internal part of $x$, instead of the largest integer $n \leq x$. If I trace the somma $\sum_{n=1}^{1000000} [\sqrt{n}] = [\sqrt{1}] + [\sqrt{2}] + \ldots + [\sqrt{999999}] + [\sqrt{1000000}]$.
[The students will use, it is believed, the following formula: $\sum_{i=1}^k i^2 = \frac{k(k+1)(2k+1)}{6}$, the demonstration is not required.]
[The students will use, it is believed, the following formula: $\sum_{i=1}^k i^2 = \frac{k(k+1)(2k+1)}{6}$, the demonstration is not required.]