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Question

tinh nhanh

M=1+1/2+1/2^2+1/2^3+...+1/2^9

Phạm Nguyễn Tất Đạt · Accepted Answer

Ta có:$M=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}$

$2M=2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}$

$2M-M=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)$

$M=2-\dfrac{1}{2^9}$

$M=\dfrac{1023}{512}$

Câu trả lời:

Ta có:$M=1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}$

$2M=2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}$

$2M-M=\left(2+1+\dfrac{1}{2}+...+\dfrac{1}{2^8}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^9}\right)$

$M=2-\dfrac{1}{2^9}$

$M=\dfrac{1023}{512}$