Consider the recurrence an=3an−1a_n = 3a_{n-1}an=3an−1 with a0=2a_0 = 2a0=2. What is the closed form for the sum ∑k=0nak\sum_{k=0}^{n} a_k∑k=0nak?
2(3n−1)2(3^n - 1)2(3n−1)
3n+1−13^{n+1} - 13n+1−1
3n+1−23^{n+1} - 23n+1−2
2⋅3n2 \cdot 3^n2⋅3n