Đáp án:

Vậy \(A=756\)

Giải thích các bước giải:

\(\frac{{0,25 \times A}}{{22}} = \frac{{27}}{6} + \frac{{27}}{{18}} + ... + \frac{{27}}{{1260}} + \frac{{27}}{{1386}}\)

Nhân cả hai vế với \(\frac{3}{{27}}\) ta được :

\(\begin{array}{l}
\frac{{0,25 \times A}}{{22}} \times \frac{3}{{27}} = \frac{{27}}{6} \times \frac{3}{{27}} + \frac{{27}}{{18}} \times \frac{3}{{27}} + ... + \frac{{27}}{{1260}} \times \frac{3}{{27}} + \frac{{27}}{{1386}} \times \frac{3}{{27}}\\
\frac{A}{{4 \times 22 \times 9}} = \frac{1}{2} + \frac{1}{6} + ... + \frac{1}{{420}} + \frac{1}{{462}}\\
\frac{A}{{792}} = \frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + ... + \frac{1}{{20 \times 21}} + \frac{1}{{21 \times 22}}\\
\frac{A}{{792}} = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{{20}} - \frac{1}{{21}} + \frac{1}{{21}} - \frac{1}{{22}}\\
\frac{A}{{792}} = 1 - \frac{1}{{22}}\\
\frac{A}{{792}} = \frac{{21}}{{22}}\\
A = \frac{{21 \times 792}}{{22}} = 756
\end{array}\)

Vậy \(A=756\)