Solve the non-homogeneous recurrence an=2an−1+2na_n = 2a_{n-1} + 2^nan=2an−1+2n with a0=1a_0 = 1a0=1.
an=(n+1)2na_n = (n+1) 2^nan=(n+1)2n
an=n2na_n = n 2^nan=n2n
an=(2n)+na_n = (2^n) + nan=(2n)+n
an=2n+1a_n = 2^{n+1}an=2n+1