Use mathematical induction to prove that 2n > n2 , for n > 5 .
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Using mathematical induction let us prove that for
Let Then and hence for the statement is true.
Suppose that the statement is true for that is
Let us prove this statement for
For this firstly let us show that for In this case and hence It follows that and thus Therefore,
Taking into acount that we conclude that
and the statement is true for
We conclue that the statement is true for all natural numbers