\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+\frac{1}{8}-....+\frac{1}{256}-\frac{1}{512}\)

\(=\frac{1}{2}-\frac{1}{512}\)

\(=\frac{255}{512}\)

Vậy \(A=\frac{255}{512}\)

=1/2-1/4+1/4-1/8+1/8-....+1/156-1/152

=1/2-1/152

=255/512

A=255/512

\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)

\(A=\frac{2-1}{4}+\frac{2-1}{8}+\frac{2-1}{16}+\frac{2-1}{32}+\frac{2-1}{64}+\frac{2-1}{128}+\frac{2-1}{256}+\frac{2-1}{512}\)

\(A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{256}-\frac{1}{512}\)

\(A=\frac{1}{2}-\frac{1}{512}\)

\(A=\frac{256}{512}-\frac{1}{512}=\frac{255}{512}\)

\(A=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}+\frac{1}{256}+\frac{1}{512}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+....+\frac{1}{256}-\frac{1}{512}\)

\(=\frac{1}{2}-\frac{1}{512}\)

\(=\frac{255}{512}\)

Vậy \(A=\frac{255}{512}\)

A=14 +18 +116 +132 +164 +1128 +1256 +1512 

=12 −14 +14 −18 +....+1256 −1512 

=12 −1512 

=255512 

Vậy A=255512 

Phạm Long Khánh

A = 255/512

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

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

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

\(A=1-\frac{1}{64}=\frac{63}{64}\)

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

=63/64

Gọi biểu thức cần tìm là A

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

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

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

\(A=1-\frac{1}{64}=\frac{63}{64}\)

Quy đồng: 32/64 - 16/64 + 8/64 - 2/64 - 1/64 = 21/64

So sánh 21/64 và 1/3: 

  Quy đồng  2 phân số trên thành: 63/192 và 64/192

Vì 63/192 < 64/192 nên 21/64 < 1/3

=> 1/2 - 1/4 + 1/8 - 1/16 +1/32 -1/64 < 1/3

2y=\(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

2y-y=1-\(\frac{1}{256}\)

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

\(\frac{255}{256}\)tik nhá ^_^ =))

  1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256

Quy đồng (MSC: 256). Ta có:

= 128/256+64/256+32/256+16/256+8/256+4/256+2/256+1/256

= 128+64+32+16+8+4+2+1/256

= 255/256

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

\(\frac{32+16+8+4+2}{64}=\frac{62}{64}=\frac{31}{32}\)

Tk mh nhé , mơn nhìu !!!
~ HOK TỐT ~

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

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

= 63/64

Ta đặt biểu thức trên là A

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

A x 2 - 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 = \(1-\frac{1}{64}\)

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

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)

\(\Rightarrow2A=\frac{2}{2}+\frac{2}{4}+\frac{2}{8}+\frac{2}{16}+\frac{2}{32}+\frac{2}{64}+\frac{2}{128}\)

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)

\(\Rightarrow2A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)

\(\Rightarrow A=1-\frac{1}{128}=\frac{128}{128}-\frac{1}{128}=\frac{127}{128}\)

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

\(=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{8}\right)+.....+\left(\frac{1}{64}-\frac{1}{128}\right)\)

\(=1-\frac{1}{128}=\frac{127}{128}\)

Đặt A = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512

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 + 1/128 x 2 + 1/256 x 2 + 1/512 x 2

2A = 1 + 1/2 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

2A - A = ( 1 + 1/2 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 )

A = 1 - 1/512

A = 511/512