An algebra problem by Vladimir Smith

Algebra Level 5

an=n+1n1(a1+a2+a3++an1) { a }_{ n }=\frac { n+1 }{ n-1 } ({ a }_{ 1 }+{ a }_{ 2 }+a_{ 3 } + \ldots +a_{ n-1 })

Consider the recurrence relation above for n2n\geq 2 and a1=1a_1 = 1 .

If a2015=b×2d a_{2015} = b \times 2 ^ d , where b b is an odd integer, then find b+2+d b + 2 + d .

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

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