tìm a: 0,25 * a/22=27/6+27/18+….+27/1260+27/1386

Đáp án:

 \(a=756\)

Giải thích các bước giải:

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

\(\begin{array}{l}
0,25 \times \frac{a}{{22}} \times \frac{3}{{27}} = \frac{{27}}{6} \times \frac{3}{{27}} + \frac{{27}}{{18}} \times \frac{3}{{27}} + … + \frac{{27}}{{1260}} \times \frac{3}{{27}} + \frac{{27}}{{1386}} \times \frac{3}{{27}}\\
\frac{a}{{792}} = \frac{1}{2} + \frac{1}{6} + … + \frac{1}{{420}} + \frac{1}{{462}}\\
\frac{a}{{792}} = \frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + … + \frac{1}{{20 \times 21}} + \frac{1}{{21 \times 22}}\\
\frac{a}{{792}} = 1 – \frac{1}{2} + \frac{1}{2} – \frac{1}{3} + … + \frac{1}{{20}} – \frac{1}{{21}} + \frac{1}{{21}} – \frac{1}{{22}}\\
\frac{a}{{792}} = 1 – \frac{1}{{22}}\\
\frac{a}{{792}} = \frac{{21}}{{22}}\\
a = \frac{{21 \times 792}}{{22}} = 756
\end{array}\)