cố gắng giúp mình nhé!
\(D=1+2+2^2+2^3+.....+2^{63}\)
\(\Leftrightarrow2D=2^1+2^2+2^3+.....+2^{63}+2^{64}\)
\(\Leftrightarrow2D-D=\left(2^1+2^2+2^3+.....+2^{63}+2^{64}\right)-\left(2^0+2^1+2^2+2^3+.....+2^{63}\right)\)
\(\Leftrightarrow D=2^{64}-1\)
Vậy.............
D = 1+2+2 mũ 2 + 2 mũ 3 + ...+2 mũ 63
2D = 2+2 mũ 2 + 2 mũ 3 + 2 mũ 4 +...+2 mũ 64
2D - D =( 2+2 mũ 2 + 2 mũ 3 + 2 mũ 4 +...+2 mũ 64) - (1+2+2 mũ 2 + 2 mũ 3 + ...+2 mũ 63)
D = 2 mũ 64 -1
\(D=1+2+2^2+2^3+...+2^{63}\)
=>\(2D=2.\left(1+2+2^2+2^3+...+2^{63}\right)\)
=>\(2D=2+2^2+2^3+...+2^{64}\)
=>\(2D-D=\left(2+2^2+2^3+...+2^{64}\right)-\left(1+2+2^2+2^3+...+2^{63}\right)\)
=>\(D=2^{64}-1\)
Vậy \(D=2^{64}-1\)
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