A =             1 + \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\)+ \(\dfrac{1}{16}\) + \(\dfrac{1}{32}\)+ \(\dfrac{1}{64}\)+ \(\dfrac{1}{128}\)

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

A \(\times\) 2 - A = 2 - \(\dfrac{1}{128}\)

A \(\times\)( 2-1) = \(\dfrac{255}{128}\)

A = \(\dfrac{255}{128}\)

Gọi \(1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\) là T

\(T=1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64}+\dfrac{1}{128}\)

\(2T=2+1+\dfrac{1}{2}+\dfrac{1}{4}+....+\dfrac{1}{64}\)

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

\(T=2+\left(1-1\right)+\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+....+\left(\dfrac{1}{64}-\dfrac{1}{64}\right)-\dfrac{1}{128}\)

\(T=2+0+0+...-\dfrac{1}{128}\)

\(T=\dfrac{256}{128}-\dfrac{1}{128}\)

\(T=\dfrac{255}{128}\)

Trả lời:

1/2+1/4+1/8+1/16=8/16+4/16+2/16+1/16=15/16   (1)

1/2+1/6+1/12+...+1/132=1/(1.2)+1/(2.3)+1/(3.4)+...+1/(11.12)

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/11-1/12)

=1-1/12=11/12  (2)

 Từ (1) và (2) => (15/16) : (11/12) = 45/44

\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}=\left(\frac{1}{2}-\frac{1}{4}\right)+\left(\frac{1}{8}-\frac{1}{16}\right)+\left(\frac{1}{32}-\frac{1}{64}\right)=\frac{1}{4}+\frac{1}{16}+\frac{1}{64}=\frac{16+4+1}{64}=\frac{21}{64}

Đặt biểu thức trên là A ta có: A= 1/2^1- 1/2^2 + 1/2^3 - 1/2^4 + 1/2^5 - 1/2^6

1/2 . A = 1/2^2 - 1/2^3 + 1/2^4 - 1/2^5 + 1/2^6 - 1/2^7

1/2 . A + A = (1/2^1- 1/2^2 + 1/2^3 - 1/2^4 + 1/2^5 - 1/2^6) + (1/2^2 - 1/2^3 + 1/2^4 - 1/2^5 + 1/2^6 - 1/2^7) = 1/2^1- 1/2^2 + 1/2^3 - 1/2^4 + 1/2^5 - 1/2^6 + 1/2^2 - 1/2^3 + 1/2^4 - 1/2^5 + 1/2^6 - 1/2^7 

từ đây những số nào trái dấu thì bạn cộng  với nhau = 0 vd như  - 1/2^2  và  1/2^2 cộng lại = 0

rút gọn xong, ta được 3/2 . A = 1/2^1 - 1/2^7 

A =  (1/2^1 - 1/2^7) . 2/3 = 1/3 - 1/2^6 < 1/3

Vậy A< 1/3

chỗ nào ko hiểu thì bạn hỏi để mình giải thích(xin lỗi vì mình trả lời hơi muộn đến bây giờ bạn chắc đã thi xong rùi ha. xin lỗi nhiều :D)

À tại sao chỗ kia đang là 1/2.a+a mà lại thành 3/2.A vậy

ý a bạn nhé

`->D` 

vì : `4/16=(4:4)/(16:4)=1/4`

      `2/8=(2:2)/(8:2)=1/4`

      `3/12=(3:3)/(12:3)=1/4`

D

\(\left(\dfrac{1}{4}\right)^{2n}=\left(\dfrac{1}{8}\right)^2\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{2.2n}=\left(\dfrac{1}{2}\right)^{3.2}\)

\(\Rightarrow\left(\dfrac{1}{2}\right)^{4n}=\left(\dfrac{1}{2}\right)^6\)

\(\Rightarrow4n=6\)

\(\Rightarrow n=\dfrac{6}{4}=\dfrac{3}{2}\)

n = 3/2

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

=>\(B=\dfrac{32}{64}+\dfrac{16}{64}+\dfrac{6}{64}+\dfrac{2}{64}+\dfrac{1}{64}\)

=>\(B=\dfrac{32+16+6+2+1}{64}\)

=>\(B=\dfrac{63}{64}\)

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

\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^6}\)

\(2B=1+\dfrac{1}{2}+...+\dfrac{1}{2^5}\)

\(\Rightarrow2B-B=1-\dfrac{1}{2^6}\)

\(\Rightarrow B=1-\dfrac{1}{2^6}=1-\dfrac{1}{64}=\dfrac{63}{64}\)

\(\frac{1}{2}\left(\frac{4}{9}-x\right)-\frac{3}{2}\left(16-x\right)+\frac{1}{2}\left(5x+10\right)=0\)

\(\Leftrightarrow\frac{2}{9}-\frac{1}{2}x-24+\frac{3}{2}x+\frac{5}{2}x+5=0\)

\(\Leftrightarrow-\frac{169}{9}=\frac{7}{2}x\Leftrightarrow x=-\frac{338}{63}\)

Sai thì thông cảm cho mk nha