Question

Tính nhanh: A= 1/2 + 1/2² + 1/2³ +...+ 1/2¹⁰

Answer 1

Đặt :

\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+..........+\dfrac{1}{2^{10}}\)

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

\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+............+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+.............+\dfrac{1}{2^{10}}\right)\)

\(A=1-\dfrac{2}{2^{10}}\)

Answer 2

Ta có :A= \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\)

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

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

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

Mình biết bao nhiêu thì mình giải bấy nhiêu chúc bạn học tốt nhé

Answer 3

Ta có :

A = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}\) (1)

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

Lấy (2) - (1), ta có :

2A - A = (\(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\)) - (\(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{20}}\))

\(\Rightarrow\) A = \(1-\dfrac{1}{2^{10}}\)

Chúc bạn học tốt!