Question

[bui thai hoc]

tim x thuoc z biet 

a,1/(1×2) + 1/(2×3) + ... + 2/(x(x+1)) = 2005/2010

Answer 1

[Đức Phạm]

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x.\left(x+1\right)}=\frac{2005}{2010}\)

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{401}{402}\)

\(\Leftrightarrow1-\frac{1}{x+1}=\frac{401}{402}\)

\(\Leftrightarrow\frac{1}{x+1}=1-\frac{401}{402}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{402}\)

\(\Leftrightarrow x+1=402\Rightarrow x=401\)