[tex] \sqrt{1 + 3 + 5 + ... + 101} = \\ [/tex]
acum scrii fiecare termen asa:
[tex]1 = 2 \times 0 + 1 \\ 3 = 2 \times 1 + 1 \\ ....... \\ 101 = 2 \times 50 + 1 \\ \sqrt{(2 \times 0 + 1) + (2 \times 1 + 1) + ... + (2 \times 50 + 1)} \\ \sqrt{(2 \times 0 + 2 \times 1 + ... + 2 \times 50) + 1 \times 51} \\ \sqrt{2(1 + 2 + ... + 50) + 51} \\ \sqrt{2 \times \frac{50 \times 51}{2} + 51 } \\ \sqrt{50 \times 51 + 51} \\ \sqrt{51(50 + 1)} \\ \sqrt{ {51}^{2} } = 51[/tex]
