Question

Giá trị biểu thức :

\(\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+....+\left(\dfrac{1}{2}\right)^{20}\) Là :

A \(\dfrac{2^{20}-1}{2^{20}}\) B.\(\dfrac{1}{2}-\dfrac{1}{2^{20}}\)

C . 1 D . \(\dfrac{2^{20}-2}{2^{20}}\)

- Ghi cách giải nữa nha!

Answer 1

\(A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+...+\left(\dfrac{1}{2}\right)^{20}\)

\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{20}}\)

\(2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{19}}\)

\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{99}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+...+\dfrac{1}{2^{20}}\right)\)

\(A=1-\dfrac{1}{2^{20}}=\dfrac{2^{20}-1}{2^{20}}\)

Chọn A