Question

tìm x:

\(\left(1-\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}\right)\cdot...\cdot\left(1-\dfrac{1}{10}\right)=\dfrac{x}{2010}\)

Answer 1

Ta có:

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{10}\right)=\dfrac{x}{2010}\)

\(\Leftrightarrow\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{9}{10}=\dfrac{x}{2010}\)

\(\Leftrightarrow\dfrac{1.2.3.....9}{2.3.4.....10}=\dfrac{x}{2010}\)

\(\Leftrightarrow\dfrac{1}{10}=\dfrac{x}{2010}\)

\(\Leftrightarrow x=\dfrac{2010}{10}\)

\(\Leftrightarrow x=201\)

Vậy x = 201

Answer 2

Thanhs bạn nha

Answer 3

\(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)....\left(1-\dfrac{1}{10}\right)=\)\(\dfrac{x}{2010}\)

\(\Leftrightarrow\) \(\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}......\dfrac{9}{10}=\dfrac{x}{2010}\)

\(\Leftrightarrow\dfrac{1.2.3......9}{2.3.4.......10}=\dfrac{x}{2010}\)

\(\Leftrightarrow\dfrac{1}{10}=\dfrac{x}{2010}\)

\(\Leftrightarrow2010=10x\)

\(\Leftrightarrow x=\dfrac{2010}{10}\)