ta có :\(\frac{1}{2^2}< \frac{1}{1.2}\)

         \(\frac{1}{3^2}< \frac{1}{2.3}\)

         \(\frac{1}{4^2}< \frac{1}{3.4}\)  

         \(............\)

        \(\frac{1}{2013^2}< \frac{1}{2012.2013}\)

cộng vế với vế ta được :

\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2013^2}< 1-\frac{1}{2013}=\frac{2012}{2013}< \frac{2014}{2013}\)

áp dụng định lí " Gedou" chất lượng hơn số lượng

\(2^{2013}< 3^{1334}\)

Làm ơn giải chi tiết giùm mik vs

Ta có: \(\frac{1}{2^2}< \frac{1}{1.2}=1-\frac{1}{2}\)

\(\frac{1}{3^2}< \frac{1}{2.3}=\frac{1}{2}-\frac{1}{3}\)

............

\(\frac{1}{2013^2}< \frac{1}{2012.2013}=\frac{1}{2012}-\frac{1}{2013}\)

=> \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2013^2}< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2012}-\frac{1}{2013}=1-\frac{1}{2013}< 1\)

=> \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2013^2}< 1\)

Mà \(\frac{2014}{2013}>1\)

=> \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2013^2}< \frac{2014}{2013}\)

1/ Ta có : \(\frac{212121}{353535}=\frac{3.7.10101}{5.7.10101}=\frac{3}{5}=\frac{42}{70}\)

\(\frac{131313}{141414}=\frac{13.10101}{14.10101}=\frac{13}{14}=\frac{65}{70}\)

Vì 42 < 65 =>  \(\frac{42}{70}<\frac{65}{70}\)  =>  \(\frac{212121}{353535}<\frac{131313}{141414}\)

2²⁰¹³< 3¹³⁴⁴

Vì 2<3

tk nhé

sai rồi

A>B nhé k nha

-Ta có: $B<1\Rightarrow B<\frac{2013^{2011}-2+2015}{2013^{2012}-2+2015}=\frac{2013^{2011}+2013}{2013^{2012}+2013}=\frac{2013(2013^{2010}+1)}{2013(2013^{2011}+1)}=\frac{2013^{2010}+1}{2013^{2011}+1}=A$

-Vậy: B<A