cho 3x-4y=7.cmr \(3x^2+4y^2\ge7\)

cho a,b,c>0 , a+b+c=1.cmr

\(\left(1+\dfrac{1}{a}\right)\left(1+\dfrac{1}{b}\right)\left(1+\dfrac{1}{c}\right)\ge64\)

cmr:

\(\dfrac{1}{9}+\dfrac{1}{16}+...+\dfrac{1}{\left(2n+1\right)^2}< \dfrac{1}{4}\left(\forall n\ge1\right)\)

n là số nguyên dương.cmr

\(\dfrac{1}{n}+\dfrac{1}{n+1}+....+\dfrac{1}{n^2}>1\)

cmr:

\(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}....\dfrac{2n-1}{2n}\le\dfrac{1}{\sqrt{3n+1}}\left(\forall n\ge1\right)\)