[tex] \frac{6}{2 \times 5} + \frac{6}{5 \times 8} + \frac{6}{8 \times 11} + ... + \frac{6}{284 \times 287} = [/tex]
[tex] = \frac{2 \times 3}{2 \times 5} + \frac{2 \times 3}{5 \times 8} + \frac{2 \times 3}{8 \times 11} + ... + \frac{2 \times 3}{284 \times 287} = [/tex]
[tex] = 2 \times (\frac{3}{2 \times 5} + \frac{3}{5 \times 8} + ... + \frac{3}{284 \times 287} ) = [/tex]
[tex] = 2 \times \frac{285}{2 \times 287} = [/tex]
[tex] = \frac{285}{287} [/tex]
[tex] \frac{3}{2 \times 5} + \frac{3}{5 \times 8} + ... + \frac{3}{284 \times 287} = [/tex]
[tex] = \frac{5 - 2}{2 \times 5} + \frac{8 - 5}{5 \times 8} + ... + \frac{287 - 284}{284 \times 287} = [/tex]
[tex] = \frac{5}{2 \times 5} - \frac{2}{2 \times 5} + \frac{8}{5 \times 8} - \frac{5}{5 \times 8} + ... + [/tex]
[tex] \frac{287}{284 \times 287} - \frac{284}{284 \times 287} = [/tex]
[tex] = \frac{1}{2} - \frac{1}{5} + \frac{1}{5} - ... + \frac{1}{284} - \frac{1}{287} = [/tex]
[tex] = \frac{1}{2} - \frac{1}{287} = [/tex]
[tex] = \frac{287}{2 \times 287} - \frac{2}{2 \times 287} = [/tex]
[tex] = \frac{287 - 2}{2 \times 287} = [/tex]
[tex] = \frac{285}{2 \times 287} [/tex]
Sper că te-am ajutat. Succes!
