Докажите, что для любого натурального числа n справедливо неравенство:
а)
[tex] \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + ... + \frac{1}{n(n + 1)} < 1[/tex]
б)
[tex] \frac{2}{(n + 2)^{2} } < \frac{1}{n + 1} - \frac{1}{n + 3} [/tex]
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