An * an + 1 = (1 / 2) n power, BN = A2N, prove that {BN} is an equal ratio sequence A1=1

If A1 = 1 is known, A2 = 1 / 2An * a (n + 1) = (1 / 2) ^ n, a (n-1) * an = (1 / 2) ^ (n-1) is divided by a (n + 1) / a (n-1) = 1 / 2, then A4 / A2 = A6 / A4 =. = 1 / 2, that is, {A2N} is an equal ratio sequence with a common ratio of 1 / 2, and the first term A2 = 1 / 2, so A2N = (1 / 2) ^ n, BN = A2N, because {A2N} is an equal ratio sequence

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