The Hogwarts Express train has reduced its one-way fare from 360360 360 360 galleons to just 270270 270 270 galleons. What is th
2 answers:
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Via the generating function method, let
Then take the recurrence,
multiply everything by
and sum over all 
:
Re-index the sums or add/remove terms as needed in order to be able to express them in terms of
:
So the recurrence relation is transformed to
For appropriate values of
, we can express the RHS in terms of geometric power series:
which tells us that
Then take the recurrence,
multiply everything by
Re-index the sums or add/remove terms as needed in order to be able to express them in terms of
So the recurrence relation is transformed to
For appropriate values of
which tells us that