Question

Bài 1. Tính nhanh giá trị của biểu thức sau:

a, E = \(\dfrac{1}{2}\)+ \(\dfrac{1}{3}\)+ \(\dfrac{1}{6}\)+ \(\dfrac{1}{24}\)+ \(\dfrac{1}{8}\)+ \(\dfrac{1}{2}\)+\(\dfrac{1}{12}\)

 

Answer 1

\(E=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{2}+\dfrac{1}{12}\)

\(E=\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{1}{8}+\dfrac{1}{12}+\dfrac{1}{24}\right)\)

\(E=\dfrac{2}{2}+\dfrac{3}{6}+\left(\dfrac{1}{8}+\dfrac{3}{24}\right)\)

\(E=1+\dfrac{1}{2}+\left(\dfrac{1}{8}+\dfrac{1}{8}\right)\)

\(E=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)+\dfrac{2}{8}\)

\(E=\dfrac{3}{2}+\dfrac{1}{4}\)

\(E=\dfrac{6}{4}+\dfrac{1}{4}\)

\(E=\dfrac{7}{4}\)