Question

1/3+1/6+1/10+1/15+....+1/x.(x+1)=4/5

Answer 1

\(\Leftrightarrow\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+\dfrac{2}{30}+...+\dfrac{2}{x\left(x+1\right)}=\dfrac{4}{5}\)

\(\Leftrightarrow2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{4}{5}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{2}{5}\)

\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{2}{5}=\dfrac{5-4}{10}=\dfrac{1}{10}\)

=>x+1=10

hay x=9

Answer 2

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