Question

Tính tổng sau đây bằng 2 cách:

\(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)

Answer 1

\(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)

\(=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+......+\dfrac{1}{2^6}\)

\(\Leftrightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+..........+\dfrac{1}{2^5}\)

\(\Leftrightarrow2A-A=\left(1+\dfrac{1}{2}+.......+\dfrac{1}{2^5}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+......+\dfrac{1}{2^6}\right)\)

\(\Leftrightarrow A=1-\dfrac{1}{2^6}\)

\(\Leftrightarrow A=\dfrac{63}{64}\)