MATH220 April 2011
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Question 07 (b)
Let be a sequence defined by
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We will prove this by induction on .
First, for , since we clearly have that
Now, let us assume that the statement is true up to , that is
and let us show that
By definition of the sequence we have that
Since ≤ 2 we have that
And since ≥ 1 we have that
These two arguments show that
and hence conclude our proof.
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