Giải thích các bước giải:
Ta có :
$1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+..+\dfrac{1}{199}-\dfrac{1}{200}$
$=(1+\dfrac{1}{3}+..+\dfrac{1}{199})-(\dfrac{1}{2}+\dfrac{1}{4}+..+\dfrac{1}{200})$
$=(1+\dfrac{1}{3}+..+\dfrac{1}{199}+\dfrac{1}{2}+\dfrac{1}{4}+..+\dfrac{1}{200})-2(\dfrac{1}{2}+\dfrac{1}{4}+..+\dfrac{1}{200})$
$=(1+\dfrac{1}{2}+\dfrac{1}{3}+..+\dfrac{1}{199}+\dfrac{1}{200})-(\dfrac{1}{1}+\dfrac{1}{2}+..+\dfrac{1}{100})$
$=\dfrac{1}{101}+\dfrac{1}{102}+..+\dfrac{1}{200}$