Question

tính :

1 / 2 + 1 / 4 + 1 / 8 + ..... + 1 / 128 + 1 / 256

Answer 1

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\)

\(Ax2=2x\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}+\frac{1}{256}\right)\)

\(Ax2=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\)

\(Ax2-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{128}\right)-\left(\frac{1}{2}-\frac{1}{4}-\frac{1}{8}-...-\frac{1}{128}-\frac{1}{256}\right)\)

\(A=1-\frac{1}{256}\)

\(A=\frac{255}{256}\)