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Let {an}\{ a_n \} {an} be a sequence defined as a0=a1=1a_0 = a_1 = 1 a0=a1=1 and an+2=2an+1+an−1 a_{n+2} = 2 a_{n+1} + a_n - 1 an+2=2an+1+an−1 for n≥0 n \ge 0 n≥0.
Find the value of this infinite summation S=∑k=0∞ak3kS = \sum_{k=0}^{\infty} \frac{a_k}{3^k} S=k=0∑∞3kak
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