# Sum of a Series - Part 2

Calculus Level 5

Let $$\{ a_n \}$$ be a sequence defined as $$a_0 = a_1 = 1$$ and $a_{n+2} = 2 a_{n+1} + a_n - n$ for $$n \ge 0$$.

Find the value of this infinite summation $S = \sum_{k=0}^{\infty} \frac{a_k}{3^k}$

×