Giải thích các bước giải:
Ta có :
$\dfrac{1}{1}-\dfrac12+\dfrac13-\dfrac14+\dfrac15-\dfrac16+...+\dfrac1{99}-\dfrac{1}{100}$
$=(\dfrac{1}{1}+\dfrac13+..+\dfrac1{99})-(\dfrac12+\dfrac14+\dfrac16+...+\dfrac{1}{100})$
$=(\dfrac{1}{1}+\dfrac13+..+\dfrac1{99})+(\dfrac12+\dfrac14+\dfrac16+...+\dfrac{1}{100})-2(\dfrac12+\dfrac14+\dfrac16+...+\dfrac{1}{100})$
$=(\dfrac{1}{1}+\dfrac12+\dfrac13+..+\dfrac1{99}+\dfrac{1}{100})-(\dfrac11+\dfrac12+\dfrac13+...+\dfrac{1}{50})$
$=\dfrac1{51}+\dfrac{1}{52}+...+\dfrac{1}{100}$
