Sửa đề:
\(A=1-\dfrac{1}{2}-\dfrac{1}{2^2}-....-\dfrac{1}{2^{10}}\)
\(A=1-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\right)\)
Đặt:
\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+....+\dfrac{1}{2^{10}}\)
\(2B=2\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{10}}\right)\)
\(2B=1+\dfrac{1}{2}+....+\dfrac{1}{2^9}\)
\(2B-B=\left(1+\dfrac{1}{2}+...+\dfrac{1}{2^9}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{10}}\right)\)
\(B=1-\dfrac{1}{2^{10}}\)
Thay vào A
\(A=1-\left(1-\dfrac{1}{2^{10}}\right)\)
\(A=\dfrac{1}{2^{10}}=\dfrac{1}{1024}\)
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