tính A =\(\frac{112}{13.20}\)+\(\frac{112}{20.27}\)+\(\frac{112}{27.34}\)+. . . . .+\(\frac{112}{62.69}\)
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Giả sử : \(\frac{a}{b}=\frac{c}{d}\) thì ad = bc
Suy ra : ad < bc thì \(\frac{a}{b}< \frac{c}{d}\) (đpcm)
a)
Có \(\frac{a}{b}< \frac{c}{d}\Rightarrow\frac{ad}{bd}< \frac{bc}{bd}\Rightarrow ad< bc\) (vì bd > 0)
Vậy \(\frac{a}{b}< \frac{c}{d}\Rightarrow ad< bc\) (với b, d > 0)
b)
Có ad < bc và bd > 0
\(\Rightarrow\frac{ad}{bd}< \frac{bc}{bd}\Rightarrow\frac{a}{b}< \frac{c}{d}\)
Vậy \(ad< bc\Rightarrow\frac{a}{b}< \frac{c}{d}\) (với b, d > 0)
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\(\left(x-1\right)^{x+2}=\left(x+1\right)^{x+4}\)
\(\left(x-1\right)^{x+2}=\left(x+1\right)^{x+2+2}\)
\(\left(x-1\right)^{x+2}=\left(x+1\right)^{x+2}.\left(x+1\right)^2\)
\(\left(x+1\right)^2=1\)
\(\Leftrightarrow\left(x+1\right)^2=1^2=\left(-1\right)^2\)
\(\Rightarrow\hept{\begin{cases}x+1=1\\x+1=-1\end{cases}\Rightarrow}\hept{\begin{cases}x=0\\x=-2\end{cases}}\)
Ta có:
\(A=\frac{112}{13.20}+\frac{112}{20.27}+.........+\frac{112}{62.69}\)
\(\Rightarrow A=112.\left(\frac{1}{13.20}+\frac{1}{20.27}+..........+\frac{1}{62.69}\right)\)
\(\Rightarrow A=16.\left(\frac{7}{13.20}+\frac{7}{20.27}+.......+\frac{7}{62.69}\right)\)
\(\Rightarrow A=16.\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+........+\frac{1}{62}-\frac{1}{69}\right)\)
\(\Rightarrow A=16.\left(\frac{1}{13}-\frac{1}{69}\right)\)
\(\Rightarrow A=16.\frac{56}{897}\)
\(\Rightarrow A=\frac{896}{897}\)
Vậy: \(A=\frac{896}{897}\)
\(A=\frac{112}{13.20}+\frac{112}{20.27}+\frac{112}{27.34}+...+\frac{112}{62.69}\)
\(\Rightarrow A=112.\left(\frac{1}{13.20}+\frac{1}{20.27}+\frac{1}{27.34}+...+\frac{1}{62.69}\right)\)
\(\Rightarrow A=112.\frac{7}{7}.\left(\frac{1}{13.20}+\frac{1}{20.27}+\frac{1}{27.34}+...+\frac{1}{62.69}\right)\)
\(\Rightarrow A=112.\frac{1}{7}\left(\frac{7}{13.20}+\frac{7}{20.27}+\frac{7}{27.34}+...+\frac{7}{62.69}\right)\)
\(\Rightarrow A=16\left(\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{27}+\frac{1}{27}-\frac{1}{34}+...+\frac{1}{62}-\frac{1}{69}\right)\)
\(\Rightarrow A=16\left(\frac{1}{13}-\frac{1}{69}\right)\)
\(\Rightarrow A=16.\frac{56}{897}\)
\(\Rightarrow A=\frac{896}{897}\)
\(Can\)\(you\) \(k\) \(for\) \(me,everyone?\)