Question

Vì mình dùng ĐT nên nó ko có ra phân số nhưng các bạn giải giúp mình câu này vs nhé (ai đúng mình tick cho) - 10h chốt nà ... :

K= 1/30 + 1/42 + 1/56 + 1/72 +1/90 + 1/110 + 1/132

Answer 1

\(K=\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\\ =\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}+\dfrac{1}{10\cdot11}+\dfrac{1}{11\cdot12}\\ =\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}\\ =\dfrac{1}{5}-\dfrac{1}{12}\\ =\dfrac{12}{60}-\dfrac{5}{60}\\ =\dfrac{7}{60}\)

Answer 2

K= \(\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}+\dfrac{1}{110}+\dfrac{1}{132}\)

K= \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+...+\dfrac{1}{11.12}\)

K=\(\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{11}-\dfrac{1}{12}\)

K= \(\dfrac{1}{5}-\dfrac{1}{12}\)

K=\(\dfrac{12}{60}\)\(-\dfrac{5}{60}\)

K=\(\dfrac{7}{60}\)