Răspuns:
625
Explicație pas cu pas:
[tex]\displaystyle 3\cdot 1 + 5\cdot 2 + 7\cdot 3 + \cdots + 19\cdot 9 + 10 = \sum_{i=1}^{9}\Big(i\cdot(2i+1)\Big) + 10\\\\ = \sum_{i=1}^{9}(2i^2 + i) + 10\\\\ = \sum_{i=1}^{9}2i^2 + \sum_{i=1}^{9} i + 10\\\\ = 2\cdot \Bigg(\sum_{i=1}^{9}i^2\Bigg) + \sum_{i=1}^{9}i + 10\\\\ = 2\cdot \frac{9\cdot (9+1)\cdot (2\cdot 9 + 1)}{6} + \frac{9\cdot (9+1)}{2} + 10\\\\ = 3\cdot 10 \cdot 19 + 9\cdot 5 + 10\\\\ = 30\cdot 19 + 45 + 10\\\\ = 570 + 55\\\\ = \boxed{625}[/tex]
