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Explicație pas cu pas:

[tex]a) \frac{1}{23} + \frac{2}{23} + ... + \frac{22}{23} = \\ = \frac{1 + 2 + ... + 22}{23} = \\ = \frac{22 \times (22 + 1) \div 2}{23} = \\ = \frac{22 \times 23}{2 \times 23} = \\ = 11 \\ b) \frac{1}{21} + \frac{2}{21} + ... + \frac{20}{21} = \\ = \frac{1 + 2 + ... + 20}{21} = \\ = \frac{20 \times (20 + 1) \div 2}{21} \\ \frac{20 \times 21}{2 \times 21} = 10[/tex]