Question

Va rog mult ex 2 din poza​

Answer 1

sper sa se inteleaga

Answer 2

Răspuns:

1/20

Explicație pas cu pas:

$S = \frac{3}{1\cdot 4} + \frac{3}{4 \cdot 7} + \frac{3}{7 \cdot 11} + ... + \frac{3}{74 \cdot 77} + \frac{3}{77 \cdot 80} = \\ = \frac{1}{1} - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{11} + ... + \frac{1}{74} - \frac{1}{77} + \frac{1}{77} - \frac{1}{80} \\ = \frac{1}{1} - \frac{1}{80} = \frac{80 - 1}{80} = \frac{79}{80}$

$\frac{2}{1\cdot 3} + \frac{2}{3 \cdot 5} + \frac{2}{5 \cdot 7} + ... + \frac{2}{71 \cdot 73} + \frac{1}{73 \cdot 75} = \\ = \frac{3 - 1}{1\cdot 3} + \frac{5 - 3}{3 \cdot 5} + \frac{7 - 5}{5 \cdot 7} + ... + \frac{73 - 71}{71 \cdot 73} + \frac{75 - 73}{73 \cdot 75} \\ = \frac{1}{1} - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + ... + \frac{1}{71} - \frac{1}{73} + \frac{1}{73} - \frac{1}{75} \\ = \frac{1}{1} - \frac{1}{75} = \frac{75 - 1}{75} = \frac{74}{75}$

$x = \sqrt{3 \cdot \Big( \frac{^{15)} 79}{80} - \frac{^{16)}74}{75} \Big)} = \sqrt{3 \cdot \frac{1185 - 1184}{1200}} = \\ = \sqrt{\frac{1}{400}} = \sqrt{ \frac{1}{ {20}^{2} } } = \bf \frac{1}{20}$