A (n) = 2A (n-1) + 1, find the general formula of a (n). Write the steps
A (n) = 2A (n-1) + 1, both sides add 1a (n) + 1 = 2A (n-1) + 2A (n) + 1 = 2 [a (n-1) + 1] let B (n) = a (n) + 1B (n) = 2B (n-1), so B (n) is an equal ratio sequence of common ratio 2, B1 = a1 + 1 = B (n) = B (1) * 2 ^ n-1, that is, a (n) = [a (1) + 1] * 2 ^ (n-1) - 1
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