Question

[Văn Nhân Cr7]

Tính 1/2^1+ 1/2^2+ 1/2^3+............. 1/2^49

Giai thich gium nhe

Answer 1

[Nguyễn Ngọc Anh Minh]

Đặt Biểu thức trên là A ta có

\(\frac{A}{2}=\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{50}}\)

\(\frac{A}{2}=A-\frac{A}{2}=\frac{1}{2}-\frac{1}{2^{50}}\Rightarrow A=1-\frac{1}{2^{49}}\)

Answer 2

[Đinh Tuấn Việt]

Đặt \(A=\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^{49}}\)

\(\Rightarrow\frac{1}{2}A=\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{50}}\)

\(\Rightarrow\frac{1}{2}A=A-\frac{1}{2}A=\frac{1}{2^1}-\frac{1}{2^{50}}\)

\(\Rightarrow A=\left(\frac{1}{2}-\frac{1}{2^{50}}\right).2=1-\frac{1}{2^{49}}\)