Question

\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)

                            Trình bày rõ ràng giúp ạ..!!! :))))))))))

Answer 1

\(2A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}\)

\(2A-A=\frac{1}{2}-\frac{1}{512}\)( Cái này dễ tự hiểu nha )

\(A=\frac{255}{512}\)

Answer 2

\(A=\frac{1}{4}+\frac{1}{8}+...+\frac{1}{512}\)

\(A=\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\)

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

\(2A-A=\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\right)-\left(\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^9}\right)\)

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

\(A=\frac{2^8}{2^9}-\frac{1}{2^9}\)

\(A=\frac{2^8-1}{2^9}\)