Question

Rút gọn B=( 1-1 phần 2).( 1- 1 phần 3).(1 phần 4)…(1- 1 phần 20)

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Answer 1

B=\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{20}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{19}{20}\)

\(=\dfrac{1.2.3....19}{2.3.4.....20}\)

\(=\dfrac{1.2.3....19:\left(2.3.....19\right)}{2.3.4.....20:\left(2.3.4.....19\right)}\)

\(=\dfrac{1}{20}\)

 

Answer 2