Question

Có ai đó giúp e với e cảm ơn.

Answer 1

\(\Leftrightarrow\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+....+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{2009}{2010}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{2009}{2010}\)

\(\Leftrightarrow-\dfrac{1}{x+1}=-\dfrac{1}{2010}\)

\(\Leftrightarrow x+1=2010\Leftrightarrow x=2009\)