1/1 nhân 2+1/2 nhân 3+1/3 nhân 4 cộng… cộng 1/x(x+1)=2010/2011 22/09/2021 Bởi Amaya 1/1 nhân 2+1/2 nhân 3+1/3 nhân 4 cộng… cộng 1/x(x+1)=2010/2011
$\frac{1}{1.2}+$ $\frac{1}{2.3}+$ $\frac{1}{3.4}+…+$ $\frac{1}{x(x+1)}=$ $\frac{2010}{2011}$ $⇒1-\frac{1}{2}+$ $\frac{1}{2}-$ $\frac{1}{2}+…+$ $\frac{1}{x}-$ $\frac{1}{x+1}=$ $\frac{2010}{2011}$ $⇒1-\frac{1}{x+1}=$ $\frac{2010}{2011}$ $⇒\frac{x}{x+1}=$ $\frac{2010}{2011}$ $⇒x=2010$ Vậy $x=2010$ Bình luận
`1/1.2+1/2.3+1/3.4+…+1/}x(x+1)}=2010/2011` `⇒1-1/2+1/2-1/3+1/3-1/4+…+1/x-1/{x+1}=2010/2011` `⇒1-1/{x+1}=2010/2011` `⇒x/{x+1}=2010/2011` `⇒x=2010` Bình luận
$\frac{1}{1.2}+$ $\frac{1}{2.3}+$ $\frac{1}{3.4}+…+$ $\frac{1}{x(x+1)}=$ $\frac{2010}{2011}$
$⇒1-\frac{1}{2}+$ $\frac{1}{2}-$ $\frac{1}{2}+…+$ $\frac{1}{x}-$ $\frac{1}{x+1}=$ $\frac{2010}{2011}$
$⇒1-\frac{1}{x+1}=$ $\frac{2010}{2011}$
$⇒\frac{x}{x+1}=$ $\frac{2010}{2011}$
$⇒x=2010$
Vậy $x=2010$
`1/1.2+1/2.3+1/3.4+…+1/}x(x+1)}=2010/2011`
`⇒1-1/2+1/2-1/3+1/3-1/4+…+1/x-1/{x+1}=2010/2011`
`⇒1-1/{x+1}=2010/2011`
`⇒x/{x+1}=2010/2011`
`⇒x=2010`