Question

B=2^2005-2^2004-2^2003-...-2-1

Answer 1

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Answer 2

\(B=2^{2005}-2^{2004}-2^{2003}-...-2-1\)

\(B=2^{2005}-\left(2^{2004}+2^{2003}+...+2+1\right)\)

Đặt \(A=2^{2004}+2^{2003}+...+2+1\)

\(2A=2\left(1+2+...+2^{2004}\right)\)

\(2A=2+2^2+...+2^{2005}\)

\(2A-A=\left(2+2^2+...+2^{2005}\right)-\left(1+2+...+2^{2004}\right)\)

\(A=2^{2005}-1\). Khi đó \(B=2^{2005}-A\)

\(\Rightarrow B=2^{2005}-\left(2^{2005}-1\right)=2^{2005}-2^{2005}+1=1\)