Giải thích các bước giải:
Ta có :
$1+\dfrac13+....+\dfrac1{101}-(\dfrac12+\dfrac14+\dfrac16+....+\dfrac1{102})$
$=(1+\dfrac13+....+\dfrac1{101})+(\dfrac12+\dfrac14+\dfrac16+....+\dfrac1{102})-2(\dfrac12+\dfrac14+\dfrac16+....+\dfrac1{102})$
$=(1+\dfrac12+\dfrac13+\dfrac14+....+\dfrac1{101}+\dfrac1{102})-2(\dfrac12+\dfrac14+\dfrac16+....+\dfrac1{102})$
$=(1+\dfrac12+\dfrac13+\dfrac14+....+\dfrac1{101}+\dfrac1{102})-(1+\dfrac12+\dfrac13+....+\dfrac1{51})$
$=\dfrac1{15}+\dfrac1{53}+...+\dfrac1{102}$