Question

a) -1/3 +2/3 -3/3 + ... - 49/3 + 50/3 b)-7/8+9/8-11/8+ ... -49/8+51/8​

Answer 1

Explicație pas cu pas:

a)

$- \frac{1}{3} + \frac{2}{3} - \frac{3}{3} + ... - \frac{49}{3} + \frac{50}{3} = \frac{ - 1 + 2 - 3 + 4 - ... - 47 + 48 - 49 + 50}{3} =$

$= \frac{ \underbrace {(- 1 + 2) + ( - 3 + 4) + ... + ( - 47 + 48) + ( - 49 + 50)}_{25 \ paranteze}}{3}$

$= \frac{1 + 1 + ... + 1}{3} = \frac{1 \cdot 25}{3} = \bf \frac{25}{3}$

b)

$- \frac{7}{8} + \frac{9}{8} - \frac{11}{8} + ... - \frac{49}{8} + \frac{51}{8} = \frac{ - 7 + 9 - 11 + 13 - ... - 49 + 51}{8} =$

$= \frac{\underbrace{(- 7 + 9) + (- 11 + 13) + ... + (- 49 + 51)}_{23 \: paranteze}}{8}$

$= \frac{2 + 2 + ... + 2}{8} = \frac{2 \cdot 23}{8} = \bf \frac{23}{4}$