Question

va rog!!
Aratati că:​

Answer 1

a)

$0.5 < \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + ... + \frac{1}{99 \times 100} < 1$

$0.5 < ( \frac{1}{1} - \frac{1}{2}) + ( \frac{1}{2} - \frac{1}{3} ) + ... + ( \frac{1}{99} - \frac{1}{100} ) < 1$

Numerele se scad între ele

$0.5 < {}^{100)} \frac{1}{1} - \frac{1}{100} < 1 \\ {}^{10)} 0.5 < \frac{100 - 1}{100} < {}^{100)} 1 \\ \frac{5}{10} {}^{(2} < \frac{99}{100} < \frac{100}{100} \\ {}^{50)} \frac{1}{2} < \frac{99}{100} < \frac{100}{100}$

$\frac{50}{100} < \frac{99}{100} < \frac{100}{100} \: \: | \times 100 \\ 50 < 99 < 100 \: Adev \breve{a}rat$