Câu hỏi của Hà Anh

Question

Tìm x biết :1/21 + 1/28 + 1/36 + ... + 2/x(x+1) = 2/9

BAN is VBN · Accepted Answer

$\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}$$\Rightarrow\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}$$\Rightarrow\frac{2}{6\cdot7}+\frac{2}{7\cdot8}+\frac{2}{8\cdot9}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}$$\Rightarrow2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}$$\Rightarrow2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}$$\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}\div2$$\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}$$\Rightarrow\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}$$\Rightarrow\frac{1}{x+1}=\frac{1}{18}$$\Rightarrow x+1=18\Rightarrow x=18-1\Rightarrow x=17$Câu trả lời: $\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}$$\Rightarrow\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}$$\Rightarrow\frac{2}{6\cdot7}+\frac{2}{7\cdot8}+\frac{2}{8\cdot9}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}$$\Rightarrow2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}$$\Rightarrow2\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}$$\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}\div2$$\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}$$\Rightarrow\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}$$\Rightarrow\frac{1}{x+1}=\frac{1}{18}$$\Rightarrow x+1=18\Rightarrow x=18-1\Rightarrow x=17$

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