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tìm x1/3+1/6+1/10+...+2/x(x+1)=2015/2017ai làm đúng mình xẽ tick

Kiệt Nguyễn · Accepted Answer

$\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Leftrightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}$$\Leftrightarrow\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{2015}{4034}$$\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{2}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{1}{2017}$$\Leftrightarrow x+1=2017$$\Leftrightarrow x=2017-1$$\Leftrightarrow x=2016$Vậy x = 2016Câu trả lời: $\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Leftrightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}=\frac{2015}{2017}.\frac{1}{2}$$\Leftrightarrow\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{2015}{4034}$$\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{2}{4034}$$\Leftrightarrow\frac{1}{x+1}=\frac{1}{2017}$$\Leftrightarrow x+1=2017$$\Leftrightarrow x=2017-1$$\Leftrightarrow x=2016$Vậy x = 2016

zZz Cool Kid_new zZz · Answer

$\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Rightarrow2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}$$\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2017}$$\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2017}$$\Rightarrow2\cdot\frac{x-1}{2\left(x+1\right)}=\frac{2015}{2017}$$\Rightarrow\frac{x-1}{2x+2}=\frac{2015}{4034}$$\Rightarrow4034x-4034=4030x+4030$$\Rightarrow4034x-4030x=8064$$\Rightarrow x=2016$Câu trả lời: $\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2017}$$\Rightarrow2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+....+\frac{1}{x\left(x+1\right)}\right)=\frac{2015}{2017}$$\Rightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2017}$$\Rightarrow2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2015}{2017}$$\Rightarrow2\cdot\frac{x-1}{2\left(x+1\right)}=\frac{2015}{2017}$$\Rightarrow\frac{x-1}{2x+2}=\frac{2015}{4034}$$\Rightarrow4034x-4034=4030x+4030$$\Rightarrow4034x-4030x=8064$$\Rightarrow x=2016$

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