bài 1 : tính nhanh a) 8/19 *5/11 +7/19*8/11 – 8/19*1/11 bài 2 : tính tổng a) 1+1/2+ 1/2^2+ 1/2^3+…+ 1/2^100

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1. Đáp án:

   1)a)=-14/209

   2)a)A=2+   1/2^101
   
   

   Giải thích các bước giải:

   Bài 1 : tính nhanh

   a) 8/19 *5/11 +7/19*8/11 – 8/19*1/11

   =8/19 *(5/11-1/11)+7/19 *8/11

   =8/19*4/11-56/209

   =32/209-56/209

   =-14/209

   Bài 2 : tính tổng a) 1+1/2+ 1/2^2+ 1/2^3+…+ 1/2^100

   A = 1 + 1/2+1/2^2+1/2^3+…+1/2^100
   2A =2 +1 +1/2+1/2^2+1/2^3+…+1/2^101
   2A – A= (2+1/2^2+1/2^3+…+1/2^101) –
   (1+1/2+1/2^2+1/2^3+…+1/2^100)
   2A -A = 2  +1/2^101

   A=2+   1/2^101

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2. $a) \dfrac{8}{19} . \dfrac{5}{11} + \dfrac{7}{19} . \dfrac{8}{11} – \dfrac{8}{19} . \dfrac{1}{11}$

   $= \dfrac{8}{19} . \dfrac{5}{11} + \dfrac{8}{19} . \dfrac{7}{11} – \dfrac{8}{19} . \dfrac{1}{11}$

   $= \dfrac{8}{19} . (\dfrac{5}{11} + \dfrac{7}{11} – \dfrac{1}{11})$

   $= \dfrac{8}{19} . \dfrac{11}{11}$

   $= \dfrac{8}{19} . 1$

   $= \dfrac{8}{19}$

   $b$)

   Đặt $A = 1 + \dfrac{1}{2} + \dfrac{1}{2^2} + \dfrac{1}{2^3} + ….. + \dfrac{1}{2^{100}}$

   $2A = 2 + 1 + \dfrac{1}{2} + \dfrac{1}{2^2} + …. + \dfrac{1}{2^{99}}$

   $2A-A= (2 + 1 + \dfrac{1}{2} + \dfrac{1}{2^2} + …. + \dfrac{1}{2^{99}})-(1 + \dfrac{1}{2} + \dfrac{1}{2^2} + \dfrac{1}{2^3} + ….. + \dfrac{1}{2^{100}})$

   $A = 2 – \dfrac{1}{2^{100}}$

   $A = \dfrac{2^{101}-1}{2^{100}}$

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