An algebra problem by Vladimir Smith

Algebra Level 5

\[ { a }_{ n }=\frac { n+1 }{ n-1 } ({ a }_{ 1 }+{ a }_{ 2 }+a_{ 3 } + \ldots +a_{ n-1 }) \]

Consider the recurrence relation above for \(n\geq 2 \) and \(a_1 = 1 \).

If \( a_{2015} = b \times 2 ^ d \), where \( b \) is an odd integer, then find \( b + 2 + d \).

Note: This problem can be solved without any calculator aids.

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