\(A=\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\\ 2A=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\\ 2A-A=\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\right)\\ A=1-\dfrac{1}{2^{10}}=\dfrac{2^{10}-1}{2^{10}}=\dfrac{1023}{1024}\)

\(A=\dfrac{1}{2}+\dfrac{1}{2}^2+\dfrac{1}{2}^3+...+\dfrac{1}{2}\)¹⁰

   \(= (\dfrac{1}{2}+\dfrac{1}{2}^9)+(\dfrac{1}{2}^2+\dfrac{1}{2}^8)+(\dfrac{1}{2}^3+\dfrac{1}{2}^7)+\dfrac{1}{2}\)¹⁰

    \(= \dfrac{257}{512}+\dfrac{65}{256}+\dfrac{17}{128}+\dfrac{1}{1024}\)

    \(=( \dfrac{514}{1024}+\dfrac{136}{1024})+(\dfrac{260}{1024}+\dfrac{1}{1024})\)

   \(=\dfrac{650}{1024}+\dfrac{261}{1024}\)

   \(=\dfrac{911}{1024}\)

Giải:

(1-1/2²).(1-1/3²).(1-1/4²).....(1-1/10²)

=3/2.2 . 8/3.3 . 15/4.4 . ... . 99/10.10

=1.3.2.4.3.5.....9.11/2.2.3.3.4.4.....10.10

=1.2.3.....9/2.3.4.....10 . 3.4.5....11/2.3.4.....10

=1/10.11/2

=11/20

Chúc bạn học tốt!

A= 1/2+1/2^2+1/2^3+....+1/2^10(1)

=> 2A = 1+1/2+1/2^2+...+1/2^9(2)

Lấy (2) - (1) ta có ;

=> A = 1-1/2^10

Vậy.................

       A = 1/2 + 1/2^2 + 1/2^3 + ...+ 1/2^10 

     2A = 1 + 1/2 + 1/2^2 + ...+ 1/2^9 

2A - A = 1 - 1/2^10 

   A     = 1 - 1/2^10 

Chúc học giỏi !!! 

2A = 1+1/2+1/2^2+...+1/2^9

2A - A = 1 - 1/2^10

A = 1 - 1/1024

A = 1024/1024 - 1/1024

A = 1023/1024

Kết quả và cách làm thì đừng lo, bảo đảm đúng

b. S=(2+4+6+...+19+20)^2

P=(3+6+9+...+30)^2

bai toan @gmail.com

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