The sequence ( b ) n ≥ 0 shall satisfy b n = ∑ k...

auto23652im

auto23652im

Answered

2022-07-14

The sequence ( b ) n 0 shall satisfy
b n = k = 0 n ( n k ) a k

Answer & Explanation

Ordettyreomqu

Ordettyreomqu

Expert

2022-07-15Added 22 answers

For every n 0, one has
b n = k = 0 n ( n k ) a k = k = 0 n ( n k ) 6 3 k + ( 1 ) k + 1 2 k 5 = 6 5 k = 0 n ( n k ) 3 k 1 5 k = 0 n ( n k ) ( 2 ) k = 6 5 ( 3 + 1 ) n 1 5 ( 1 2 ) n = 6 4 n ( 1 ) n 5
which satisfies the recursion
b n + 2 = 3 b n + 1 + 4 b n

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