Ta có:
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{x}\right)=\frac{1}{2010}\)
\(\Rightarrow\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{x-1}{x}=\frac{1}{2010}\)
\(\Rightarrow\frac{1.2.3....\left(x-1\right)}{2.3.4....x}=\frac{1}{2010}\)
Ta đơn giản đi hết sẽ còn:
\(\Rightarrow\frac{1}{x}=\frac{1}{2010}\Leftrightarrow x=2010\)
dễ vái :)))
.....<=>1/2.2/3.3/4.4/5.....(x-1)/x=1/2010 <=> 1/x =1/2010 <=> x=2010