Question

1 supra 2•3+1 supra 3•4+......+1 supra 33•34​

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{1}{2 \cdot3} + \frac{1}{3 \cdot4} + ... + \frac{1}{33 \cdot34} = \\ \frac{3 - 2}{2 \cdot3} + \frac{4 - 3}{3 \cdot4} + ... + \frac{34 - 33}{33 \cdot34} = \\ \frac{3}{2 \cdot3} - \frac{2}{2 \cdot3} + \frac{4}{3 \cdot4} - \frac{3}{3 \cdot4} + ... + \frac{34}{33 \cdot34 } - \frac{33}{33 \cdot34} = \\ \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} + ... + \frac{1}{33} - \frac{1}{34} = \\ \frac{ ^{17)} 1}{2} - \frac{1}{34} = \frac{17}{34} - \frac{1}{34} = \frac{ {16}^{(2} }{34} = \boxed{ \bold{ \frac{8}{17} }}$