Question

[Lê Huyền My]

Làm hộ mik câu c,d với. Cảm ơn trước ạ

Answer 1

[Yen Nhi]

c) \(\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{6}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

\(=\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{3}+\frac{1}{6}\right)+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

\(=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\) (1)

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\) (2)

Ta có: (2) - (1) được: \(A=1-\frac{1}{128}\Rightarrow A=\frac{127}{128}\)

Answer 2

[Yen Nhi]

d) \(\left(3-\frac{1}{4}+\frac{2}{3}\right)-\left(5+\frac{1}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)

\(=3-\frac{1}{4}+\frac{2}{3}-5-\frac{1}{3}+\frac{6}{5}-6+\frac{7}{4}-\frac{3}{2}\)

\(=\left(3-5-6\right)+\left(\frac{7}{4}-\frac{1}{4}-\frac{3}{2}\right)+\left(\frac{2}{3}-\frac{1}{3}\right)+\frac{6}{5}\)

\(=-8+\frac{7-1-6}{4}+\frac{1}{3}+\frac{6}{5}\)

\(=\frac{1}{3}+\frac{6}{5}-8=\frac{5+18-120}{15}=\frac{-97}{15}\)