Question

cele doua ex dau coroana si 50 de puncte​

Answer 1

Răspuns:

1275

Explicație pas cu pas:

$n \geqslant 1, \ \ n < \sqrt{n \cdot (n + 1)} < n + 1 \\ \implies \Big[ \sqrt{n \cdot (n + 1)}\Big] = n$

$\Big[ \sqrt{1 \cdot 2} \Big] = 1 \\ \Big[ \sqrt{2 \cdot 3} \Big] = 2 \\...... \\ \Big[ \sqrt{50 \cdot 51} \Big] = 50$

$\Big[ \sqrt{1 \cdot 2} \Big] + \Big[ \sqrt{2 \cdot 3} \Big] + ... + \Big[ \sqrt{50 \cdot 51} \Big] = \\ = 1 + 2 + ... + 50 = \frac{50 \cdot 51}{2} = 25 \cdot 51 = \bf 1275$

q.e.d.