Question

Tính giá trị của biểu thức:

   \(M=512-\frac{512}{2}-\frac{512}{2^2}-....-\frac{512}{2^{10}}\)

Answer 1

\(M=512-\frac{512}{2}-\frac{512}{2^2}-...-\frac{512}{2^{10}}\)

\(M=512-512.\left(\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{10}}\right)\)

Đặt\(S=\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^{10}}\)

=> \(\frac{1}{2}S=\frac{1}{2^2}-\frac{1}{2^3}-...-\frac{1}{2^{11}}\)

=> \(\frac{1}{2}S-S=-\frac{1}{2}S=\frac{1}{2^{11}}-\frac{1}{2}\)

=> \(S=\left(\frac{1}{2^{11}}-\frac{1}{2}\right):-\frac{1}{2}\)