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Question

$\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{998}{1000}$tìm x nhé

ST · Accepted Answer

$\Rightarrow\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{1}{2}\cdot\frac{998}{1000}$$\Rightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{499}{1000}$$\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{499}{1000}$$\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{499}{1000}$$\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{499}{1000}$$\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{499}{1000}$$\Rightarrow\frac{1}{x+1}=\frac{1}{1000}$=>x+1=1000=>x=999Câu trả lời: $\Rightarrow\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{1}{2}\cdot\frac{998}{1000}$$\Rightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{499}{1000}$$\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{499}{1000}$$\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{499}{1000}$$\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{499}{1000}$$\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{499}{1000}$$\Rightarrow\frac{1}{x+1}=\frac{1}{1000}$=>x+1=1000=>x=999

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