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\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\)
\(2\times A=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\)
\(2\times A-A=\left(1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}\right)\)
\(A=1-\frac{1}{128}\)
\(A=\frac{127}{128}\)
\(B=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\)
\(2\times B=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\)
\(B=1-\frac{1}{16}=\frac{15}{16}\)
\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(\Leftrightarrow4\times x+\frac{15}{16}=1\)
\(\Leftrightarrow4\times x=\frac{1}{16}\)
\(\Leftrightarrow x=\frac{1}{64}\)
a, 5.3x=405 b, 2x:8=4 c, x64 = x d, 2x.4=128
3x=81 2x =32 => x=1 2x =32
3x=34 2x=25 2x=25
=> x = 4 => x = 5 => x = 5
a)320 + ( 218-x)=475
( 218-x)=475-320
( 218-x)=155
x =218-155
x =63
b)315-6/x=275
6/x=315-275
6/x=40
x=40.6
x=240
c)4*(x-15)+32=64
4*(x-15) =64-32
4*(x-15) = 32
4*(x-15) =32:4
4*(x-15) =8
(x-15) =8:4
(x-15) =2
x =2+15
x =17
\(\frac{127}{128}\times x=1\)
\(\Rightarrow x=\frac{128}{127}\)