Question

\(A=\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+...+\left(\dfrac{1}{2}\right)^{10}\)

Tính giúp mình và giải hộ mk luôn nhé

Answer 1

\(A=\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+\left(\dfrac{1}{2}\right)^4+.......+\left(\dfrac{1}{2}\right)^{10}\)

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

\(\Leftrightarrow2A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+.....+\dfrac{1}{2^9}\)

\(\Leftrightarrow2A-A=\left(\dfrac{1}{2}+\dfrac{1}{2^2}+.........+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2^2}+\dfrac{1}{2^3}+.....+\dfrac{1}{2^{10}}\right)\)

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