Đáp án:
\(a=756\)
Giải thích các bước giải:
Nhân cả hai vế với \(\dfrac{{3}}{27}\) ta được:
$0,25 \times \dfrac{a}{{22}} \times \dfrac{3}{{27}}=$
$\dfrac{{27}}{6} \times \dfrac{3}{{27}} + \dfrac{{27}}{{18}} \times \dfrac{3}{{27}} + ... + \dfrac{{27}}{{1260}} \times \dfrac{3}{{27}} + \dfrac{{27}}{{1386}} \times \dfrac{3}{{27}}$
$\Rightarrow \dfrac{a}{{792}} = \dfrac{1}{2} + \dfrac{1}{6} + ... + \dfrac{1}{{420}} + \dfrac{1}{{462}}$
$\Rightarrow \dfrac{a}{{792}} = \dfrac{1}{{1 \times 2}} + \dfrac{1}{{2 \times 3}} + ... + \dfrac{1}{{20 \times 21}} + \dfrac{1}{{21 \times 22}}$
$\Rightarrow \dfrac{a}{{792}} = 1 - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + ... + \dfrac{1}{{20}} - \dfrac{1}{{21}} + \dfrac{1}{{21}} - \dfrac{1}{{22}}$
$\Rightarrow \dfrac{a}{{792}} = 1 - \dfrac{1}{{22}}$
$\Rightarrow \dfrac{a}{{792}} = \dfrac{{21}}{{22}}$
$\Rightarrow a = \dfrac{{21 \times 792}}{{22}} = 756 $
