- #1
Topgun_68
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Homework Statement
Consider the sequence n1, n2, n3, ... that satisfies the recurrence relation nk = nk-1 / k + 1 for all integers k ≥ 2 with the initial condition that n1 = 1. Find the explicit formula nk for the nth term of the sequence?
2. The attempt at a solution
I calculated out the terms for n = 1, n = 2, n = 3 & n = 4 but there is no obvious relation that I can see because of the decimal numbers. For example:
Starting variable n1 = 1 so..
n2 = [itex]\frac{1}{3}[/itex] = .333
n3 = [itex]\frac{.333}{4}[/itex] = .08325
n4 = [itex]\frac{.08325}{5}[/itex] = .01665
Any hints on how to calculate the explicit formula for nk?
Thanks for any info!