Question

Tính :

E = \(\dfrac{1}{90}\) - \(\dfrac{1}{72}\) - \(\dfrac{1}{56}\) - \(\dfrac{1}{42}\) - \(\dfrac{1}{30}\) - \(\dfrac{1}{20}\) - \(\dfrac{1}{12}\) - \(\dfrac{1}{6}\) - \(\dfrac{1}{2}\)

Answer 1

E=\(\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\\ E=\dfrac{1}{90}-\left(\dfrac{1}{72}+\dfrac{1}{56}+\dfrac{1}{42}+\dfrac{1}{30}+\dfrac{1}{20}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{2}\right)\\ E=\dfrac{1}{90}-\left(\dfrac{1}{9.8}+\dfrac{1}{8.7}+\dfrac{1}{7.6}+\dfrac{1}{6.5}+\dfrac{1}{5.4}+\dfrac{1}{4.3}+\dfrac{1}{3.2}+\dfrac{1}{2.1}\right)\\ E=\dfrac{1}{90}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\\ E=\dfrac{1}{90}-\left(1-\dfrac{1}{9}\right)\\ E=\dfrac{1}{90}-\dfrac{8}{9}\\ E=\dfrac{1}{90}-\dfrac{80}{90}\\ E=-\dfrac{79}{90}\)Vậy:\(E=-\dfrac{79}{90}\)

Answer 2

E=\(\dfrac{1}{10.9}-\dfrac{1}{9.8}-\dfrac{1}{8.7}-\dfrac{1}{7.6}-\dfrac{1}{6.5}-\dfrac{1}{5.4}-\dfrac{1}{4.3}-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

E=\(\dfrac{1}{10}-\dfrac{1}{1}\)

E=\(\dfrac{-9}{10}\)

Answer 3

E = \(\dfrac{1}{10.9}-\dfrac{1}{9.8}-\dfrac{1}{8.7}-\dfrac{1}{7.6}-\dfrac{1}{6.5}-\dfrac{1}{5.4}-\dfrac{1}{4.3}-\dfrac{1}{3.2}-\dfrac{1}{2.1}\)

E=\(\dfrac{1}{10}-\dfrac{1}{9}-\dfrac{1}{9}-\dfrac{1}{8}-\dfrac{1}{8}-\dfrac{1}{7}-\dfrac{1}{7}-\dfrac{1}{6}-\dfrac{1}{6}-\dfrac{1}{5}-\dfrac{1}{5}-\dfrac{1}{4}-\dfrac{1}{4}-\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{1}{1}\)

E = \(\dfrac{1}{10}-\dfrac{1}{3}\)

E = \(\dfrac{-7}{30}\)

Answer 4

E= -7/30