Question

[Nguyễn Phương Linh]

Tính : P=512-512/2-512/2^2-512/2^3-.....-512/2^10 .

Answer 1

[Trên con đường thành công không có....]

Ta có:

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

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

Đặt \(A=\frac{512}{2}+\frac{512}{2^2}+\frac{512}{2^3}+...+\frac{512}{2^{10}}\)

\(\Rightarrow2A=512+\frac{512}{2}+\frac{512}{2^2}+...+\frac{512}{2^9}\)

\(\Rightarrow2A-A=512-\frac{512}{2^{10}}\)

\(\Rightarrow A=512-\frac{512}{2^{10}}\)

\(\Rightarrow P=512-A=512-\left(512-\frac{512}{2^{10}}\right)=\frac{512}{2^{10}}=\frac{1}{2}\)

Answer 2

[Vũ Minh Tuấn]

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

\(\Rightarrow P=2^9-\frac{2^9}{2}-\frac{2^9}{2^2}-\frac{2^9}{2^3}-...-\frac{2^9}{2^{10}}\)

\(\Rightarrow P=2^9-2^8-2^7-2^6-...-\frac{1}{2}\)

\(\Rightarrow2P=2^{10}-2^9-2^8-2^7-...-1\)

\(\Rightarrow2P-P=2^{10}-2^9-2^8-2^7-...-1-\left(2^9-2^8-2^7-2^6-...-\frac{1}{2}\right)\)

\(\Rightarrow2P-P=2^{10}-2^9-2^8-2^7-...-1-2^9+2^8+2^7+2^6+...+\frac{1}{2}\)

\(\Rightarrow P=2^{10}-2^9-2^9+\frac{1}{2}\)

\(\Rightarrow P=2^{10}-2.2^9+\frac{1}{2}\)

\(\Rightarrow P=2^{10}-2^{10}+\frac{1}{2}\)

\(\Rightarrow P=0+\frac{1}{2}\)

\(\Rightarrow P=\frac{1}{2}.\)

Chúc bạn học tốt!