a) A = ($\frac{1}{2}$ + 1) . ($\frac{1}{3}$ + 1) . ($\frac{1}{4}$ + 1) . ... . ($\frac{1}{2019}$ + 1) . ($\frac{1}{2020}$ + 1)
= $\frac{3}{2}$ . $\frac{4}{3}$ . $\frac{5}{4}$ . ... . $\frac{2020}{2019}$ . $\frac{2021}{2020}$
= $\frac{3 . 4 . 5 . ... . 2020 . 2021}{2 . 3 . 4 . ... . 2019 . 2020}$
= $\frac{2021}{2}$
b) B = $\frac{1}{56}$ + $\frac{1}{72}$ + ... + $\frac{1}{210}$
= $\frac{1}{7.8}$ + $\frac{1}{8.9}$ + ... + $\frac{1}{14.15}$
= $\frac{1}{7}$ - $\frac{1}{8}$ + $\frac{1}{8}$ - $\frac{1}{9}$ + ... + $\frac{1}{14}$ - $\frac{1}{15}$
= $\frac{1}{7}$ - $\frac{1}{15}$
= $\frac{8}{105}$
Chúc học tốt!!!
