Question

tính giá trị biểu thức sau một cách hợp lí :

\(A=\dfrac{-10}{3}+\dfrac{19}{6}.\dfrac{7}{5}-\dfrac{19}{3}.\dfrac{1}{10}+\dfrac{19}{10}.\dfrac{4}{3}\)

\(M=\dfrac{1+2+2^2+2^3+....+2^{2012}}{2^{2014}-2}\)

Answer 1

\(A=\dfrac{-10}{3}+\dfrac{19}{6}\cdot\dfrac{7}{5}-\dfrac{19}{3}\cdot\dfrac{1}{10}+\dfrac{19}{10}\cdot\dfrac{4}{3}\)

\(=\dfrac{-10}{3}+\dfrac{19}{3}\cdot\dfrac{7}{10}-\dfrac{19}{3}\cdot\dfrac{1}{10}+\dfrac{19}{3}\cdot\dfrac{4}{10}\)

\(=\dfrac{-10}{3}+\dfrac{19}{3}\cdot\left(\dfrac{7}{10}-\dfrac{1}{10}+\dfrac{4}{10}\right)\)

\(=\dfrac{-10}{3}+\dfrac{19}{3}\cdot\dfrac{10}{10}=\dfrac{-10}{3}+\dfrac{19}{3}\)

\(=\dfrac{9}{3}=3\)