If Sn=2Sn−1−1S_n = 2S_{n-1} - 1Sn=2Sn−1−1 with S0=0S_0 = 0S0=0, where Sn=∑k=1nakS_n = \sum_{k=1}^n a_kSn=∑k=1nak, which recurrence does ana_nan satisfy for n≥2n \geq 2n≥2?
an=an−1a_n = a_{n-1}an=an−1
an=2an−1a_n = 2a_{n-1}an=2an−1
an=an−1+1a_n = a_{n-1} + 1an=an−1+1
an=Sn−1a_n = S_{n-1}an=Sn−1