Nè !!! Ai biết làm thì giúp mình nhá !!! Cho K = $\frac{1}{2}$x $\frac{3}{4}$x $\frac{5}{6}$x…..x$\frac{97}{98}$x $\frac{99}{100}$ Hãy so sánh K v

0 bình luận về “Nè !!! Ai biết làm thì giúp mình nhá !!! Cho K = $\frac{1}{2}$x $\frac{3}{4}$x $\frac{5}{6}$x…..x$\frac{97}{98}$x $\frac{99}{100}$ Hãy so sánh K v”

1. Đáp án:

   Ta có: 

   $\dfrac{1}{2}=\dfrac{1}{2}$; $\dfrac{3}{4}>\dfrac{2}{3}$; $\dfrac{5}{6}>\dfrac{4}{5}$; … ; $\dfrac{99}{100}>\dfrac{98}{99}$

   Suy ra 

   $\dfrac{1}{2}\times\dfrac{3}{4}\times\dfrac{5}{6}\times…\times\dfrac{99}{100}>\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{4}{5}\times…\times\dfrac{98}{99}$

   $\left(\dfrac{1}{2}\times\dfrac{3}{4}\times\dfrac{5}{6}\times…\times\dfrac{99}{100}\right)\times\left(\dfrac{1}{2}\times\dfrac{3}{4}\times\dfrac{5}{6}\times…\times\dfrac{99}{100}\right)>\left(\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{4}{5}\times…\times\dfrac{98}{99}\right)\times\left(\dfrac{1}{2}\times\dfrac{3}{4}\times\dfrac{5}{6}\times…\times\dfrac{99}{100}\right)$

   $K\times K>\dfrac{1}{2}\times\dfrac{1}{2}\times\left(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\times…\times\dfrac{99}{100}\right)$

   $K\times K>\dfrac{1}{4}\times\dfrac{2\times3\times4\times…\times99}{3\times4\times5\times…\times99\times100}$

   $K\times K>\dfrac{1}{4}\times\dfrac{2}{100}$

   $K\times K>\dfrac{1}{200}>\dfrac{1}{225}$

   $K\times K>\dfrac{1}{15}\times\dfrac{1}{15}$

   Vậy $K>\dfrac{1}{15}$

   Bình luận