Consider the recurrence an=2an−1−1a_n = 2a_{n-1} - 1an=2an−1−1 with a0=2a_0 = 2a0=2. What is the closed-form expression for ana_nan?
an=2n+1a_n = 2^n + 1an=2n+1
an=2n+na_n = 2^n + nan=2n+n
an=2n+1−1a_n = 2^{n+1} - 1an=2n+1−1
an=3⋅2n−1a_n = 3 \cdot 2^n - 1an=3⋅2n−1