Question

Thu gọn

A = (2 + 1)(2^2 + 1)(2^4 + 1)x...x(2^32 + 1) - 2^64

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Answer 1

\(A=1\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{32}+1\right)-2^{64}\)

\(=...\)

\(=\left(2^{32}-1\right)\left(2^{32}+1\right)-2^{64}\)

\(=2^{64}-1-2^{64}=-1\)