Đáp án:
$42\,925$
Giải thích các bước giải:
Ta có:
$\begin{array}{l}\quad S = 1^2 + 2^2 + 3^3 + \dots + n^2\\ \to S = 1 + 2(1+1) + 3(2+1) + \dots + n(n-1+1)\\ \to S = 1 + 1.2 + 2 + 2.3 +3 +\dots + (n-1)n + n\\ \to S = (1 + 2 +3 + \dots + n) + (1.2 + 2.3 +\dots + (n-1)n)\\ \to S = \dfrac{n(n+1)}{2} + \dfrac{(n-1)n(n+1)}{3}\\ \to S = \dfrac{3n(n+1) + 2n(n+1)(n-1)}{6}\\ \to S = \dfrac{n(n+1)(2n+1)}{6}\\ Với\,\,n = 50\,\,ta\,\,được:\\ \quad S = \dfrac{50.(50+1)(2.50 +1)}{6}\\ \to S = \dfrac{50.51.101}{6}\\ \to S = 42\,925 \end{array}$
