Răspuns:
1275
Explicație pas cu pas:
[tex]n \geqslant 1, \ \ n < \sqrt{n \cdot (n + 1)} < n + 1 \\ \implies \Big[ \sqrt{n \cdot (n + 1)}\Big] = n[/tex]
[tex]\Big[ \sqrt{1 \cdot 2} \Big] = 1 \\ \Big[ \sqrt{2 \cdot 3} \Big] = 2 \\...... \\ \Big[ \sqrt{50 \cdot 51} \Big] = 50[/tex]
[tex]\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 [/tex]
q.e.d.
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Verified answer
Răspuns:
1275
Explicație pas cu pas:
[tex]n \geqslant 1, \ \ n < \sqrt{n \cdot (n + 1)} < n + 1 \\ \implies \Big[ \sqrt{n \cdot (n + 1)}\Big] = n[/tex]
[tex]\Big[ \sqrt{1 \cdot 2} \Big] = 1 \\ \Big[ \sqrt{2 \cdot 3} \Big] = 2 \\...... \\ \Big[ \sqrt{50 \cdot 51} \Big] = 50[/tex]
[tex]\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 [/tex]
q.e.d.