cho \(\frac{a}{b}=\frac{c}{d}\) Chúng minh rằng
\(\frac{2005a-2006b}{2006c+2007d}=\frac{2005c-2006d}{2006a+2007b}\)
Cho a,b,c, thuộc R và a,b,c khác 0 thỏa mãn \(^{b^2}\) =ac .CMR: \(\frac{a}{b}\) =\(\frac{\left(a+2007b\right)^2}{\left(b+2007c\right)^2}\)
cho \(\dfrac{a}{b}=\dfrac{c}{d}\)
CMR
a, \(\dfrac{a+2006}{a-2006}=\dfrac{c+2006d}{c-2006d}\)
b, \(\dfrac{2006\left(a+c\right)}{2006a}=\dfrac{b+c}{b}\)
CMR: \(\frac{1}{5}< \frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{6}-\frac{1}{7}< \frac{2}{5}\)
CMr: \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}>\frac{5}{8}\)
CMR: \(A=\frac{1}{3}+\frac{2}{3^2}+...+\frac{100}{3^{100}}< \frac{1}{4}\)
CMR:
\(\frac{7}{12}< \frac{1}{41}+\frac{1}{42}+\frac{1}{43}+.........+\frac{1}{79}+\frac{1}{80}< \frac{5}{6}\)
CMR: \(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+\frac{3.4-1}{4!}+...+\frac{99.100-1}{100!}< 2\)
CMR nếu \(\frac{a+2}{a-2}=\frac{b+3}{b-3}thì\frac{a}{2}=\frac{b}{3}\)
