Every Skywalker serves either the light side or the dark side.

The first Skywalker serves the dark side.

For n ? 2, the nth Skywalker serves the same side as the (n ? 1)st Skywalker with probability 1/4, and the opposite side with probability 3/4.

Let d_n be the probability that the nth Skywalker serves the dark side.

(a) Express d_n with a recurrence equation and sufficient base cases.

(b) Give a simple closed formula for d_n

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