Sum of a Series

Calculus Level 5

Let {an}\{ a_n \} be a sequence defined as a0=a1=1a_0 = a_1 = 1 and an+2=2an+1+an1 a_{n+2} = 2 a_{n+1} + a_n - 1 for n0 n \ge 0 .

Find the value of this infinite summation S=k=0ak3kS = \sum_{k=0}^{\infty} \frac{a_k}{3^k}

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