tìm phân số tối giản:x/y

Đáp án:

\(x = 108\)

Giải thích các bước giải:

\(\begin{array}{l}
\quad \dfrac{63}{23\times 27} + \dfrac{63}{27\times 31} + \cdots+ \dfrac{63}{1123\times 1127}\\
= \dfrac{63}{4}\left(\dfrac{4}{23\times 27} + \dfrac{4}{27\times 31} + \cdots+ \dfrac{4}{1123\times 1127}\right)\\
= \dfrac{63}{4}\left(\dfrac{27 - 23}{23\times 27} + \dfrac{31 -27}{27\times 31} + \cdots+ \dfrac{1127 - 1123}{1123\times 1127}\right)
= \dfrac{63}{4}\left(\dfrac{1}{23} - \dfrac{1}{27} + \dfrac{1}{27}  - \dfrac{1}{31} + \cdot + \dfrac{1}{1123} - \dfrac{1}{1127}\right)\\
= \dfrac{63}{4}\left(\dfrac{1}{23} - \dfrac{1}{1127}\right)\\
= \dfrac{63}{4}\times \dfrac{48}{1127}\\
= \dfrac{108}{161}\\
\text{Vậy}\ x = 108
\end{array}\)