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1/h=1/2(1/a+1/b)=1/2a+1/2b=(a+b)/2ab
=>(a+b/)2ab-1/h=0
quy dong len ta co
(a+b)h/2abh-2ab/2abh=0=> (ah+bh-2ab)/2abh=0 =>ah+bh-2ab=0
=>ah+bh-ab-ab=0
=>a(h-b)-b(a-h)=0
=>a(h-b)=b(a-h)
=>a/b=(a-h)(h-b)
\(\frac{a}{-3}=\frac{b}{4};\frac{b}{2}=\frac{c}{3}=>\frac{a}{-3}=\frac{b}{4}=\frac{2}{6}\)
áp dụng tính chất DTSBN ta có
\(\frac{a}{-3}=\frac{b}{4}=\frac{c}{6}=\frac{a+b+c}{-3+4+6}=\frac{14}{7}=2\)
\(+\frac{a}{-3}=>a=-6\)
\(+\frac{b}{4}=2=>b=8\)
\(+\frac{c}{6}=2=>c=12\)
Ta có;\(\frac{a}{-3}=\frac{b}{4};\frac{b}{2}=\frac{c}{3}\Leftrightarrow\frac{b}{4}=\frac{c}{6}\Rightarrow\frac{a}{-3}=\frac{b}{4}=\frac{c}{6}\)
Áp dụng tính chất dãy tỉ số băng nhau:
\(\frac{a}{-3}=\frac{b}{4}=\frac{c}{6}=\frac{a+b+c}{-3+4+6}=\frac{14}{7}=2\)
Vậy\(\hept{\begin{cases}a=2\cdot\left(-3\right)=-6\\b=2\cdot4=8\\c=2\cdot6=12\end{cases}}\)
a/\(\left(2-x\right)\times-3=\left(3x-1\right)\times4\)4
\(\Rightarrow-6+3x=12x-4\)
\(\Rightarrow-2=9x\)
\(\Rightarrow x=\frac{-2}{9}\)
bài b cx tương tự nha
ta có;\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}=\frac{a+b}{c+d}\)(THEO TÍNH CHẤT DÃY TỈ SỐ BẰNG NHAU)
\(\Rightarrowđpcm\)
Ta có :
\(C=\frac{2-1}{2!}+\frac{3-1}{3!}+\frac{4-1}{4!}+...+\frac{n-1}{n!}\)
\(=\left(\frac{2}{2!}+\frac{3}{3!}+\frac{4}{4!}+...+\frac{n}{n!}\right)-\left(\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+...+\frac{1}{n!}\right)\)
\(=\left(1+\frac{1}{2!}+\frac{1}{3!}+....+\frac{1}{\left(n-1\right)!}\right)-\left(\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+....+\frac{1}{n!}\right)\)
\(=1+\frac{1}{2!}+\frac{1}{3!}+....+\frac{1}{\left(n-1\right)!}-\frac{1}{2!}-\frac{1}{3!}-\frac{1}{4!}-....-\frac{1}{n!}\)
\(=1-\frac{1}{n!}=\frac{n!-1}{n!}\)
\(C=\frac{2}{4.7}-\frac{3}{5.9}+\frac{2}{7.10}-\frac{3}{9.13}+...+\frac{2}{301.304}-\frac{3}{401.405}\)
\(C=\left(\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{301.304}\right)-\left(\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{401.405}\right)\)
\(C=\frac{2}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{301.304}\right)-\frac{3}{4}\left(\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{401.405}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+..+\frac{1}{401}-\frac{1}{405}\right)\) \(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{405}\right)\)
\(C=\frac{25}{152}-\frac{4}{27}\)
\(C=\frac{67}{4104}\)
ra 67/1014