Question

1/5 + 1/10+ 1/ 20+1/40+.......+1/1280

Tính nhanh nha bạn.Nhanh lên nha,mình cần gấp lắm.

Answer 1

\(A=\frac{1}{1.5}+\frac{1}{2.5}+\frac{1}{4.5}+...+\frac{1}{256.5}\)

\(A=\frac{1}{5}\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\right)\)

\(5A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\)

\(\frac{5}{2}A=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}+\frac{1}{2^9}\)

\(\Rightarrow5A-\frac{5}{2}A=1-\frac{1}{2^9}\)

\(\Rightarrow\frac{5}{2}A=1-\frac{1}{2^9}\)

\(\Rightarrow A=\frac{2}{5}\left(1-\frac{1}{2^9}\right)=\frac{2}{5}-\frac{1}{5.2^8}\)

Answer 2