Question

[Hoàng Ngọc Tuyết Nung]

cmr

\(\dfrac{1}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{4017}{2013^2.2014^2}< 1\)

Answer 1

[Manh Nhu]

Ta thấy 3²-2²=5; 4²-3²=7;......;2014²-2013²=(2014-2013)(2014+2013)=4017

=> VT=1/4+1/4-1/9+1/9-1/16+1/16-......-1/2013²+1/2013²-1/2014²

=1/4+1/4-1/2014=1/2-1/2014²<1/2<1