\(1\dfrac{1}{3};1\dfrac{1}{8};1\dfrac{1}{15};1\dfrac{1}{15};1\dfrac{1}{24};1\dfrac{1}{35};...\)
\(\Leftrightarrow\dfrac{4}{3};\dfrac{9}{8};\dfrac{16}{15};\dfrac{25}{24};\dfrac{36}{35};...\)
\(\Leftrightarrow\dfrac{2^2}{1.3};\dfrac{3^2}{2.4};\dfrac{4^2}{3.5};\dfrac{5^2}{4.6};\dfrac{6^2}{5.7};...\)
\(\Rightarrow\) Tích 100 số hạng đầu tiên của dãy là:
\(\dfrac{2^2}{1.3}.\dfrac{3^2}{2.4}.\dfrac{4^2}{3.5}.\dfrac{5^2}{4.6}.\dfrac{6^2}{5.7}......\dfrac{101^2}{100.102}\)
\(=\dfrac{2.3.4.5.6....101}{1.2.3.4.5.....100}.\dfrac{2.3.4.5.6....101}{3.4.5.6.7....102}\)
\(=101.\dfrac{2}{102}\)\(=\dfrac{101}{51}\)
Vậy..............................
~ học tốt ~
