Question

9/2 +9/4+9/8+....+9/128+9/256

Answer 1

Ta có : \(\frac{9}{2}+\frac{9}{4}+\frac{9}{8}+....+\frac{9}{128}+\frac{9}{256}\)

\(=9.\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+....+\frac{1}{128}+\frac{1}{256}\right)\)

\(=9.\left(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+......+\left(\frac{1}{128}-\frac{1}{256}\right)\right)\)

\(=9.\left(1-\frac{1}{256}\right)\)

\(=9.\frac{255}{256}=\frac{2295}{256}\)