Câu hỏi của Aquarius

Question

Tính $\dfrac{3}{4}$.$\dfrac{8}{9}$.$\dfrac{15}{16}$. ... .$\dfrac{9999}{10000}$

Nguyễn Bảo Trung · Accepted Answer

$\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.....\dfrac{9999}{10000}$

$=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{99.101}{100.100}$

$=\dfrac{\left(1.2.3.....99\right)}{\left(2.3.4.....100\right)}.\dfrac{\left(3.4.5.....101\right)}{\left(2.3.4.....100\right)}$

$=\dfrac{1}{100}.\dfrac{101}{2}=\dfrac{101}{200}$Câu trả lời: $\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}.....\dfrac{9999}{10000}$

$=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}.....\dfrac{99.101}{100.100}$

$=\dfrac{\left(1.2.3.....99\right)}{\left(2.3.4.....100\right)}.\dfrac{\left(3.4.5.....101\right)}{\left(2.3.4.....100\right)}$

$=\dfrac{1}{100}.\dfrac{101}{2}=\dfrac{101}{200}$