Question

[𝓐𝓼𝓾𝓷𝓪]

                                                                  mik gấp lắm làm đc bài nào thì làm nha!
 

Answer 1

[Victorique de Blois]

\(D=\frac{1}{2\cdot5}+\frac{1}{5\cdot8}+\frac{1}{8\cdot11}+...+\frac{1}{1979\cdot1982}\)

\(D=\frac{1}{3}\left(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+...+\frac{3}{1979\cdot1982}\right)\)

\(D=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{1979}-\frac{1}{1982}\right)\)

\(D=\frac{1}{3}\left(\frac{1}{2}-\frac{1}{1982}\right)=\frac{165}{991}\)

gọi d là ƯC(12n + 1; 30n + 2)

\(\Rightarrow\hept{\begin{cases}12n+1⋮d\\30n+2⋮d\end{cases}\Rightarrow\hept{\begin{cases}5\left(12n+1\right)⋮d\\2\left(30n+2\right)⋮d\end{cases}}\Rightarrow\hept{\begin{cases}60n+5⋮d\\60n+4⋮d\end{cases}}}\)

=> 60n + 5 - 60n - 4 ⋮ d

=> 1 ⋮ d

=> d = +-1

=> ps đó tối giản

Answer 2

[𝓐𝓼𝓾𝓷𝓪]

thanks nha kb ko