Răspuns:
x = 2
Explicație pas cu pas:
[tex] \frac{1}{1 \times 3} = \frac{1}{2} \times ( \frac{2}{1} - \frac{4}{3} ) \\ \frac{1}{3 \times 5} = \frac{1}{2} \times ( \frac{4}{3} - \frac{6}{5}) \\ ... \\ \frac{1}{61 \times 63} = \frac{1}{2} \times ( \frac{62}{61} - \frac{64}{63} )[/tex]
[tex]x \times \frac{1}{2} \times ( \frac{2}{1} - \frac{4}{3} + \frac{4}{3} - \frac{6}{5} + ... + \frac{62}{61} - \frac{64}{63} ) = 2 - \frac{64}{63} [/tex]
[tex]x \times \frac{1}{2} \times (\frac{2}{1}-\frac{64}{63}) = 2 - \frac{64}{63} [/tex]
[tex] \frac{x}{2} \times (2-\frac{64}{63}) = 2 - \frac{64}{63}[/tex]
[tex] \frac{x}{2} = 1 = > x = 2[/tex]
