1.Tính A = 3/5 . 4/7 – 2/7 . 3/5 – 3/5 . 6/7 B = (1+ 1/1.3) . (1+ 1/2.4) . (1+ 1/3.2) ……. (1+ 1/98.100)

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1. Đáp án:

   $A=-\dfrac{12}{35}$

   $B=1,98$

   Giải thích các bước giải:

   $A=\dfrac{3}{5}.\dfrac{4}{7}-\dfrac{2}{7}.\dfrac{3}{5}-\dfrac{3}{5}.\dfrac{6}{7}\\=\dfrac{3}{5}\left ( \dfrac{4}{7}-\dfrac{2}{7}-\dfrac{6}{7} \right )\\=\dfrac{3}{5}.\dfrac{-4}{7}=-\dfrac{12}{35}\\B=\left ( 1+\dfrac{1}{1.3} \right )\left ( 1+\dfrac{1}{2.4} \right )\left ( 1+\dfrac{1}{3.5} \right )…\left ( 1+\dfrac{1}{98.100} \right )\\=\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}…\dfrac{9801}{9800}\\=\dfrac{(2.2).(3.3).(4.4)…(99.99)}{(1.3).(2.4).(3.5)…(98.100)}\\=\dfrac{2.99}{100}=1,98$

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2. Đáp án:

    

   Giải thích các bước giải:

    1 Tính 

   A = $\frac{3}{5}$ . $\frac{4}{7}$ – $\frac{2}{7}$ . $\frac{3}{5}$ – $\frac{3}{5}$ . $\frac{6}{7}$ 

   ⇒ A = $\frac{3}{5}$ . { $\frac{4}{7}$ – $\frac{2}{7}$ – $\frac{6}{7}$ }

   ⇒ A = $\frac{3}{5}$ . $\frac{-4}{7}$

   ⇒ A = $\frac{-12}{35}$

   B = {1 + $\frac{1}{1.3}$ } . {1 + $\frac{1}{2.4}$ } . {1 + $\frac{1}{3.2}$ } …. {1 + $\frac{1}{98.100}$ } 

   ⇒ B = $\frac{4}{3}$ . $\frac{9}{8}$ . $\frac{16}{15}$ …. $\frac{9801}{9800}$

   ⇒B = $\frac{(2.2) . ( 3 . 3 ) ( 4 . 4 ) … ( 99 . 99 ) }{(1.3).(2.4).(3.5)…(98.100) }$  

   ⇒ B = $\frac{2.99}{100}$ = $\frac{198}{100}$ = $\frac{99}{50}$ 

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