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

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

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

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

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

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

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

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

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​+

nhân A lên 2A sau đó lấy 2A-A là đc :

2A =1+1/2+.....+1/32

2A-A=(1+1/2+.....+1/32)-(1/2+1/4+.....+1/32+1/64)

A=1-1/64

A=63/64

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

\(2A=\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)\times2\)

\(2A=\frac{1}{2}\times2+\frac{1}{4}\times2+\frac{1}{8}\times2+\frac{1}{16}\times2+\frac{1}{32}\times2+\frac{1}{64}\times2\)

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

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

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

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

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

`=> 2A = 2(1/2 + 1/4 + 1/8 + 1/16+ 1/32 + 1/64)`

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

`=>A =2A -A =1+1/2 +1/4 +1/8+1/16 +1/32-1/2-1/4-1/8-1/16-1/32 -1/64`

`A = 1-1/64 = 64/64 -1/64 =63/64`

A = (2 + 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1) - 2⁶⁴

A = (2 - 1)(2 + 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1) - 2⁶⁴

A = (2² - 1)(2² + 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1) - 2⁶⁴

A = (2⁴ - 1)(2⁴ + 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1) - 2⁶⁴

A = (2⁸ - 1)(2⁸ + 1)(2¹⁶ + 1)(2³² + 1) - 2⁶⁴

A = (2¹⁶ - 1)(2¹⁶ + 1)(2³² + 1) - 2⁶⁴

A = (2³² - 1)(2³² + 1) - 2⁶⁴

A = 2⁶⁴ - 1 - 2⁶⁴

A = -1

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

\(\dfrac{32}{64}+\dfrac{16}{64}+\dfrac{8}{64}+\dfrac{4}{64}+\dfrac{2}{64}+\dfrac{1}{64}=\dfrac{32+16+8+4+2+1}{64}=\dfrac{63}{64}\)

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

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

 =                         63/64

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

\(2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{18}+\dfrac{1}{32}\right)-\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}\right)\)

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

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

giúp em với ạ , em cấn gấp ,  4h em học rồi ạ . Cảm ơn những ai giúp em ạ , em tick luôn ạ

= 63/64 nha

Lời giải:

$A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}$

$2\times A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}$

$2\times A-A=(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32})-(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64})$

$A=1-\frac{1}{64}=\frac{63}{64}$

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

 2A = 2.(1/2+1/4+1/8+1/16+1/32+1/64)
            = 1 + 1/2+1/4+1/8+1/16+1/32
=> 2A - A = (1+1/2+1/4+1/8+1/16+1/32) - (1/2+1/4+1/8+1/16+1/32+1/64)
=> A = 1 - 1/64
         = 63/64

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

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

\(\Rightarrow2A-A=1-\frac{1}{64}\)

\(\Rightarrow A=\frac{63}{64}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+..+\frac{1}{32}-\frac{1}{64}\)

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

\(A=\frac{63}{64}\)Đây là cách 1

\(Ax2=1+\left(\frac{1}{2}+...+\frac{1}{64}\right)-\frac{1}{64}\)

\(Ax2=1+A-\frac{1}{64}\)

\(Ax2-A=1-\frac{1}{64}\)

\(A=\frac{63}{64}\)Đây là cách 2

P/s: Làm 1 cách đc kh???

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

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

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

2A - A = ( 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 )

A = 1 -  1/64

A = 63/64