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

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1. Đáp án:

    

   Giải thích các bước giải:

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

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

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

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

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

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

   $B$ $=$ $\dfrac{15}{23}$ 

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2. Đáp án:

    $B=\frac{15}{23}$

   Giải thích các bước giải:

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

   $⇒B=\frac{2}{3}(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+….+\frac{3}{43.46})$

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

   $⇒B=\frac{2}{3}(1-\frac{1}{46})$

   $⇒B=\frac{2}{3}.\frac{45}{46}$

   $⇒B=\frac{90}{138}=\frac{15}{23}$

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