Đặt A = $\frac{27}{6}+\frac{27}{18}+...+\frac{27}{1260}+\frac{27}{1386}$
$\begin{align}
& A\times \frac{3}{27}=\frac{27}{6}\times \frac{3}{27}+\frac{27}{18}\times \frac{3}{27}+...+\frac{27}{1260}\times \frac{3}{27}+\frac{27}{1386}\times \frac{3}{27} \\
& A\times \frac{3}{27}=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{420}+\frac{1}{462} \\
& A\times \frac{3}{27}=\frac{1}{1\times 2}+\frac{1}{2\times 3}+...+\frac{1}{20\times 21}+\frac{1}{21\times 22} \\
& A\times \frac{3}{27}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{20}-\frac{1}{21}+\frac{1}{21}-\frac{1}{22} \\
& A\times \frac{3}{27}=1-\frac{1}{22}=\frac{21}{22} \\
& A=\frac{21}{22}:\frac{3}{27}=\frac{189}{22} \\
\end{align}$
Vậy $\frac{0,25\times a}{22}=\frac{189}{22}\Rightarrow 0,25\times a=189\Rightarrow a=189:0,25=756$