Question

Considere as diferenças:
a) Determine o valor da soma

b) Calcule a soma

Answer 1

a) Determine o valor da soma
$1 - \frac{1}{2} = \frac{2 - 1}{2} = \frac{1}{2}$
$\frac{1}{2} - \frac{1}{3} = \frac{3 - 2}{6} = \frac{1}{6}$
$\frac{1}{3} - \frac{1}{4} = \frac{4 - 3}{12} = \frac{1}{12}$
$\frac{1}{4} - \frac{1}{5} = \frac{5 - 4}{20} = \frac{1}{20}$
$\frac{1}{5} - \frac{1}{6} = \frac{6 - 5}{30} = \frac{1}{30}$
b) Calcule a soma
$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \frac{1}{4 \times 5} + \frac{1}{5 \times 6} =$
$\frac{1}{3} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} =$
m.m. c(3,6,12,20,30)=60
$\frac{20 + 10 + 5 + 3 + 2}{60} = \frac{40}{60}$
simplificando o resultado fica
$\frac{40 \div 20}{60 \div 20} = \frac{2}{3}$