Tính nhanh : `B = 2/{1.4} + 2/{4.7} + 2/{7.10}+ …… +2/{43.46}`

Đáp án:

Giải thích các bước giải:

 $B$ $=$ $\dfrac{2}{1.4}$ $+$ $\dfrac{2}{4.7}$ $+$ $\dfrac{2}{7.10}$ $+$ $…$ $+$ $\dfrac{2}{43.46}$

$B$ $=$ $\dfrac{2}{3}$ $($ $\dfrac{1}{1.4}$ $+$ $\dfrac{1}{4.7}$ $+$ $\dfrac{1}{7.10}$ $+$ $…$ $+$ $\dfrac{1}{43.46}$ $)$

$B$ $=$ $\dfrac{2}{3}$ $($ $\dfrac{1}{1}$ $-$ $\dfrac{1}{4}$ $+$ $\dfrac{1}{4}$ $-$ $\dfrac{1}{7}$ $+$ $\dfrac{1}{7}$ $-$ $\dfrac{1}{10}$ $+$ $…$ $+$ $\dfrac{1}{43}$ $-$ $\dfrac{1}{46}$ $)$

$B$ $=$ $\dfrac{2}{3}$ $($ $\dfrac{1}{1}$ $-$ $\dfrac{1}{46}$ $)$

$B$ $=$ $\dfrac{2}{3}$ $ .$ $\dfrac{45}{46}$

$B$ $=$ $\dfrac{2.45}{3.46}$ $=$ $\dfrac{2.15.3}{3.2.23}$ 

$B$ $=$ $\dfrac{15}{23}$