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Ta có :
\(S=\left(\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\frac{31}{32}+\frac{63}{64}+\frac{127}{128}\right)-6\)
\(S=\left(\frac{64}{128}+\frac{102}{128}+\frac{112}{128}+\frac{120}{128}+\frac{124}{128}+\frac{126}{128}+\frac{127}{128}\right)-6\)
\(S=\frac{64+102+112+120+124+126+127}{128}-6\)
\(S=\frac{775}{128}-6\)
\(S=\frac{775}{128}-\frac{768}{128}\)
\(S=\frac{7}{128}\)
S=1/2+3/4+7/8+15/16+31/32+63/64+127/128 -6
S= 1-1/2 + 1-1/4 + 1-1/8 + 1-1/16 + 1-1/32 + 1-1/64+ 1-1/128 - 6
S= (1+1+1+1+1+1+1-6)- (1/2+1/4+1/8+1/16 + 1/32+1/64+1/128)
S= 1- 111/128
S= 17/128
(Làm lụi nha bn)
(\(\frac{-7}{15}\)) . \(\frac{5}{8}\).\(\frac{15}{-7}\). (-32)
=\(\frac{-7}{24}\). \(\frac{480}{7}\)
= -20
Q=\(\dfrac{1}{2}+\left(\dfrac{3}{4}+\dfrac{7}{8}\right)+\left(\dfrac{15}{16}+\dfrac{31}{32}\right)+\left(\dfrac{63}{64}+\dfrac{127}{128}\right)-6\)
Q=\(\dfrac{1}{2}+\dfrac{13}{8}+\dfrac{61}{32}+\dfrac{253}{128}\)\(-6\)
Q= \(\dfrac{64}{128}+\dfrac{208}{128}+\dfrac{244}{128}+\dfrac{253}{128}-6\)
Q= \(\dfrac{769}{128}-6\)
Q=\(\dfrac{769}{128}-\dfrac{768}{128}\)
Q= \(\dfrac{1}{128}\)
(-7/15) . 5/8 . 15/-7 . (-32)
=( -7/15 . 15/-7 ) . [ 5/8 . (-32)]
= 1 . ( -20 )
= -20
\(\frac{14^{16}\cdot21^{31}\cdot35^{48}}{10^{16}\cdot15^{32}\cdot7^{96}}\)
\(=\frac{\left(2\cdot7\right)^{16}\cdot\left(3\cdot7\right)^{31}\cdot\left(5\cdot7\right)^{48}}{\left(2\cdot5\right)^{16}\cdot\left(3\cdot5\right)^{32}\cdot\left(7^2\right)^{48}}\)
\(=\frac{2^{16}\times3^{31}\times5^{48}\times7^{95}}{2^{16}\times3^{32}\times5^{48}\times7^{96}}\)
\(=\frac{1\times1}{3\times7}\)
\(=\frac{1}{21}\)
\(\dfrac{15}{34}+\dfrac{7}{21}+\dfrac{19}{34}-\dfrac{32}{17}+\dfrac{2}{3}\)
\(=\left(\dfrac{15}{34}+\dfrac{19}{34}\right)+\dfrac{7}{21}+\dfrac{-32}{17}+\dfrac{2}{3}\)
\(=1+\dfrac{1}{3}+\dfrac{-32}{17}+\dfrac{2}{3}\)
\(=1+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\dfrac{-32}{17}\)
\(=1+1+\dfrac{-32}{17}\)
\(2+\dfrac{-32}{17}=\dfrac{2}{17}\)
-(-31/32-7/15)+(-15/32-7/15)
=689/480+(-449/480)
=1/2
HT