Câu hỏi của Đỗ Diệp Anh

Question

Tìm x;

a,$\left(1-\dfrac{1}{3}\right)$*$\left(1-\dfrac{1}{6}\right)$*$\left(1-\dfrac{1}{10}\right)$*...*$\left(1-\dfrac{1}{780}\right)$*x=1

Linh Trần · Accepted Answer

Ta có:

$\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{780}\right).x=1$

$\Leftrightarrow\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}.....\dfrac{779}{780}.x=1$

$\Leftrightarrow\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}.....\dfrac{1558}{1560}.x=1$

$\Leftrightarrow\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}.......\dfrac{38.41}{39.40}.x=1$

$\Leftrightarrow\dfrac{1.4.2.5.3.6.....38.41}{2.3.3.4.4.5.....39.40}.x=1$

$\Leftrightarrow\dfrac{\left(1.2.3.4....38\right)\left(4.5.6.7....41\right)}{\left(2.3.4.....39\right)\left(3.4.5....40\right)}.x=1$

$\Leftrightarrow\dfrac{1}{39}.\dfrac{41}{3}.x=1$

$\Leftrightarrow\dfrac{41}{117}.x=1$

$\Leftrightarrow x=\dfrac{117}{41}$

Vậy ...Câu trả lời: Ta có: