Question

[Hà Khánh Giang]

(𝔁 +\(\dfrac{1}{2}\)) + (𝔁 +\(\dfrac{1}{4}\)) + (𝔁 +\(\dfrac{1}{8}\)) + ... + (𝔁 +\(\dfrac{1}{1024}\)) = 1

Ai lm đúng mik sẽ kb nnha!

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Answer 1

[Nguyễn Lê Phước Thịnh]

Số số hạng là 10-1+1=10(số)

Đặt \(A=\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{1024}\)

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

=>\(2A=1+\dfrac{1}{2}+...+\dfrac{1}{2^9}\)

=>\(2A-A=1+\dfrac{1}{2}+...+\dfrac{1}{2^9}-\dfrac{1}{2}-\dfrac{1}{2^2}-...-\dfrac{1}{2^{10}}\)

=>\(A=1-\dfrac{1}{2^{10}}=\dfrac{1023}{1024}\)

\(\left(x+\dfrac{1}{2}\right)+\left(x+\dfrac{1}{4}\right)+...+\left(x+\dfrac{1}{1024}\right)=1\)

=>\(\left(x+x+x+...+x\right)+\left(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{10}}\right)=1\)

=>\(10x+\dfrac{1023}{1024}=1\)

=>\(10x=\dfrac{1}{2024}\)

=>\(x=\dfrac{1}{20240}\)

Answer 2

[Hà Khánh Giang]

Hầu như lúc nào mik hỏi lên đều là bn lm trc tiên lun á Thịnh¯\_(ツ)_/¯