Question

Tính nhanh:

 A= 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

Answer 1

\(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\)

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

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

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

\(A=\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+..\left(\dfrac{1}{32}-\dfrac{1}{32}\right)+\left(1-\dfrac{1}{64}\right)\)

\(A=1-\dfrac{1}{64}\)

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

Answer 2

\(\dfrac{127}{128}\)

Answer 3

A=21​+41​+91​+161​+321​+641​

42�=42⋅(12+14+18+116+132+164)24​A=24​⋅(21​+41​+81​+161​+321​+641​)

2�=1+12+14+18+116+1322A=1+21​+41​+81​+161​+321​

2�−�=(1+12+14+18+116+132)−(12+14+18+116+132+164)2A−A=(1+21​+41​+81​+161​+321​)−(21​+41​+81​+161​+321​+641​)

�=(12−12)+(14−14)+..(132−132)+(1−164)A=(21​−21​)+(41​−41​)+..(321​−321​)+(1−641​)

�=1−164A=1−641​

�=6364A=6463​