Question

[Vongola Tsuna]

Tính Giá trị biểu thức 

\(512-\frac{512}{2}-\frac{512}{2^2}-\frac{512}{^{2^3}}-...-\frac{512}{2^{10}}\)

Answer 1

[Hoàng Phúc]

\(512-\frac{512}{2}-\frac{512}{2^2}-\frac{512}{2^3}-......-\frac{512}{2^{10}}\)

\(=512.\left(1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-....-\frac{1}{2^{10}}\right)\)

Đặt \(A=1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-....-\frac{1}{2^{10}}\)

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

\(=>2A-A=\left(2-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^9}\right)-\left(1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-....-\frac{1}{2^{10}}\right)\)

\(=>A=2-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^9}-1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{10}}\)

\(=>A=2-1-1+\frac{1}{2^{10}}=\frac{1}{2^{10}}\)

\(=>512-\frac{512}{2}-\frac{512}{2^2}-...-\frac{512}{2^{10}}=512.\frac{1}{2^{10}}=\frac{512}{2^{10}}=\frac{1}{2}\)

Answer 2

[Đinh Đức Hùng]

\(=512\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

\(=512\left(1-\frac{1}{2^{10}}\right)=512.\frac{1023}{1024}=\frac{1023}{512}\)