Question

a) Tìm số tự nhiên x biết : \(\left(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+...+\dfrac{1}{8\cdot9\cdot10}\right)\cdot x=\dfrac{23}{45}\)

b) Tìm các số tự nhiên a ; b; c ; d biết : \(\dfrac{30}{43}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

Answer 1

Phân tích phân số \(\dfrac{30}{43}\) ta có:

\(\dfrac{30}{43}=\dfrac{1}{\dfrac{43}{30}}=\dfrac{1}{1+\dfrac{13}{30}}=\dfrac{1}{1+\dfrac{1}{\dfrac{30}{13}}}=\dfrac{1}{1+\dfrac{1}{2+\dfrac{4}{13}}}\)

\(=\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{\dfrac{13}{4}}}}=\dfrac{1}{1+\dfrac{1}{2+\dfrac{1}{3+\dfrac{1}{4}}}}=\dfrac{1}{a+\dfrac{1}{b+\dfrac{1}{c+\dfrac{1}{d}}}}\)

Vậy: \(\left\{{}\begin{matrix}a=1\\b=2\\c=3\\d=4\end{matrix}\right.\)