Question

Найдите последовательно значение каждой из разностей:

Answer 1

$frac{1}{2} - frac{1}{3} = frac{3-2}{6} = frac{1}{6}$
$frac{1}{3} - frac{1}{4} = frac{4-3}{12} = frac{1}{12}$
$frac{1}{4} - frac{1}{5} = frac{5-4}{20} = frac{1}{20}$
$frac{1}{5} - frac{1}{6} = frac{6-5}{30} = frac{1}{30}$
$frac{1}{6} - frac{1}{7} = frac{7-6}{42} = frac{1}{42}$
$frac{1}{7} - frac{1}{8} = frac{8-7}{56} = frac{1}{56}$
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$frac{1}{6} + frac{1}{12} + frac{1}{20} + frac{1}{42} + frac{1}{56} = frac{2+1}{12} + frac{1}{20} + frac{1}{42} + frac{1}{56} = frac{1}{4} + frac{1}{20} + frac{1}{42} + frac{1}{56} = frac{5+1}{20} + frac{3}{10} + frac{1}{42} + frac{1}{56} = frac{21+5}{210} + frac{1}{56} = frac{26}{210} + frac{1}{56} = frac{52+7.5}{420} = frac{59.5}{420}$