In the sequence {an}, A1 = 1 / 2, an + 1 = an = 1 / (4N ^ 2-1), find the general term formula of {an}

Because an + 1-an = 1 / (4N ^ 2-1) = 1 / 2 * [1 / (2n-1) - 1 / (2n + 1)], so a2-a1 = 1 / 2 * (1-1 / 3) a3-a2 = 1 / 2 * (1 / 3-1 / 5):: an-an-1 = 1 / 2 * [(1 / 2n-3) - 1 / (2n-1)], and then A1 = 1 / 2, so an = 1 / 2 + 1 / 2 * [1-1 / (2n-1)]

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