Question

Tìm F:

F=3/4.8/9. ... .9999/1000

Answer 1

\(F=\frac{3}{4}\cdot\frac{8}{9}\cdot........\cdot\frac{9999}{1000}\)

\(F=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot....\cdot\frac{99.101}{100.100}\)

\(F=\frac{1}{2}.\frac{101}{100}=\frac{101}{200}\)

_Hắc phong_

Answer 2

\(\frac{3}{4}.\frac{8}{9}.....\frac{9999}{10000}\)

\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.....\frac{99.101}{100.100}\)

\(=\frac{1.2.3.....99}{2.3.4.....100}.\frac{3.4.5.....101}{2.3.4.....100}=\frac{1}{100}.\frac{101}{2}\)

\(=\frac{101}{200}\)