Đáp án:
Giải thích các bước giải:
$A= \dfrac{3}{2}+ \dfrac{7}{6}+ \dfrac{13}{12}+...+ \dfrac{10101}{10100}$
$= \dfrac{2+ 1}{2}+ \dfrac{6+ 1}{6}+ \dfrac{12+ 1}{12}+...+ \dfrac{10100+ 1}{10100}$
$= (1+ \dfrac{1}{2})+ (1+ \dfrac{1}{6})+ (1+ \dfrac{1}{12})+...+ (1+ \dfrac{1}{10100})$
$= (1+ \dfrac{1}{1. 2})+ (1+ \dfrac{1}{2. 3})+ (1+ \dfrac{1}{3. 4})+...+ (1+ \dfrac{1}{100. 101})$
$= (1+ 1+ 1+...+ 1)+ (\dfrac{1}{1. 2}+ \dfrac{1}{2. 3}+ \dfrac{1}{3. 4}+...+ \dfrac{1}{100. 101})$
$= 100+ (1- \dfrac{1}{2}+ \dfrac{1}{2}- \dfrac{1}{3}+ ... + \dfrac{1}{100}- \dfrac{1}{101})$
$= 100+ 1- \dfrac{1}{101}= 101- \dfrac{1}{101}< 101= B$
$⇒ A< B$
