Prove that the sum of the first n odd natural numbers is .
That is to prove the following:
Prove this by using mathematical induction.
For, the left hand side is 1 and right hand side is
So, the statement is true for .
Assume that is true.
Prove that, the statement is true for.
That is, to prove that
The left hand side is as follows:
By inductive hypothesis
Therefore, the left hand side is equal to right hand side.
That is the above statement is true for .
Hence, from the principle of mathematical induction, write as follows:
Thus, the sum of the first n odd natural numbers is .
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