Ta có:
Vì : $\dfrac{1}{5^{2}}$ $<$ $\dfrac{1}{4.5}$
$\dfrac{1}{6^{2}}$ $<$ $\dfrac{1}{5.6}$
..........
$\dfrac{1}{100^{2}}$ $<$ $\dfrac{1}{99.100}$
Nên $B$ $<$ $\dfrac{1}{4.5}$ $+$ $\dfrac{1}{5.6}$ $+$ $...$ $+$ $\dfrac{1}{99.100}$
⇒ $B$ $<$ $\dfrac{1}{4}$ $-$ $\dfrac{1}{5}$ $+$ $\dfrac{1}{5}$ $-$ $\dfrac{1}{6}$ $+$ $...$ $+$ $\dfrac{1}{99}$ - $\dfrac{1}{100}$
⇒ $B$ < $\dfrac{1}{4}$ $-$ $\dfrac{1}{100}$ <$\dfrac{1}{4}$ ( vì $\dfrac{1}{100}$ $>$ $0$)
Vậy $B$ $<$ $\dfrac{1}{4}$
Chúc bạn học tốt!
