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Omni-MATH / Define the sequence x_(i)_(i≥0) by x₀=2009 and x_(n)=−(2009)/(n)∑_(k=0)^(n−1)x_(k) for all n≥1. Compute the value of ∑_(n=0)²⁰⁰⁹2^(n)x_(n) · Discussion

Discussing Define the sequence {x_(i)}_(i≥0) by x₀=2009 and x_(n)=−(2009)/(n)∑_(k=0)^(n−1)x_(k) for all n≥1. Compute the value of ∑_(n=0)²⁰⁰⁹2^(n)x_(n) · Omni-MATH

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