Đáp án:
Giải thích các bước giải:
$A= 1+ \dfrac{1}{3}+ \dfrac{1}{6}+ \dfrac{1}{10}+...+ \dfrac{1}{4950}$
$ \dfrac{1}{2}A= \dfrac{1}{2}. ( \dfrac{1}{3}+ \dfrac{1}{6}+ \dfrac{1}{10}+...+ \dfrac{1}{4950})$
$\dfrac{1}{2}A= \dfrac{1}{6}+ \dfrac{1}{12}+ \dfrac{1}{20}+...+ \dfrac{1}{9900}$
$\dfrac{1}{2}A= \dfrac{1}{2. 3}+ \dfrac{1}{3. 4}+ \dfrac{1}{4. 5}+....+ \dfrac{1}{99. 100}$
$\dfrac{1}{2}A= \dfrac{1}{2}- \dfrac{1}{3}+ \dfrac{1}{3}- \dfrac{1}{4}+ \dfrac{1}{4}- \dfrac{1}{5}+...+ \dfrac{1}{99}- \dfrac{1}{100}$
$\dfrac{1}{2}A=\dfrac{1}{2}- \dfrac{1}{100}$
$\dfrac{1}{2}A= \dfrac{49}{100}$
$A= \dfrac{49}{100}: \dfrac{1}{2}$
$A= \dfrac{49}{50}$
