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\(=\dfrac{1}{2}-\left(\dfrac{1}{3\cdot7}+\dfrac{1}{7\cdot11}+...+\dfrac{1}{23\cdot27}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{23\cdot27}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{23}-\dfrac{1}{27}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{9-1}{27}\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{8}{27}=\dfrac{1}{2}-\dfrac{2}{27}=\dfrac{27-4}{54}=\dfrac{23}{54}\)
\(\frac{27}{23}\)+ \(\frac{5}{15}\)+ \(\frac{3}{7}\)-\(\frac{4}{23}\)- \(\frac{12}{9}\)= \(\frac{27}{23}\)+ \(\frac{1}{3}\)+ \(\frac{3}{7}\)-\(\frac{4}{23}\)- \(\frac{4}{3}\)
= (\(\frac{27}{23}\)- \(\frac{4}{23}\)) + (\(\frac{1}{3}\)- \(\frac{4}{3}\)) + \(\frac{3}{7}\)
= 1+ (-1) + \(\frac{3}{7}\)= \(\frac{3}{7}\)
Ta có : \(127^{23}< 128^{23}nênsuyra:128^{23}=\left(2^7\right)^{23}=2^{161}\)
\(513^{15}>512^{15}nênsuyra:512^{15}=\left(2^9\right)^{15}=2^{135}\)
suy ra : \(127^{23}< 2^{161}< 2^{135}< 513^{15}\)
vậy suy ra \(127^{23}< 513^{15}\)
\(-\dfrac{15}{23}:\dfrac{22x}{7}=-\dfrac{14x}{11}:\left(13+\dfrac{4}{5}\right)\)
=>\(-\dfrac{15}{23}\cdot\dfrac{7}{22x}=\dfrac{-14x}{11}:\dfrac{69}{5}\)
=>\(-\dfrac{105}{23\cdot22x}=\dfrac{-70x}{11\cdot69}\)
=>\(\dfrac{-3}{2x}=\dfrac{-2x}{3}\)
=>\(4x^2=9\)
=>\(x^2=\dfrac{9}{4}\)
=>\(\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{matrix}\right.\)
S= (-23) + ( -415) + 7 +15
S = -438 + 7 + 15
S = -431 + 15
S = -416
S = -416
NHÁ ^_^