Consider that for any integer (n), (2n+1) is an odd number.
By expansion and collecting terms, (2n+1)^2 = ______.
Since _______ is an integer it follows that (2n+1)^2 is odd.
Therefore the square of any odd number is also an odd number.
Show that the square of an oddnumber is an odd number using a direct proof.
2 answers
any odd number can be written in the form 2n + 1 , where n is a positive integer.
(2n+1)^2 = 4n^2 + 4n + 1
= 4(n^2 + 1) + 1
since any integer multiplied by 4 is even, the term 4(n^2 + 1) is even , adding 1 to it would make it odd.
(2n+1)^2 = 4n^2 + 4n + 1
= 4(n^2 + 1) + 1
since any integer multiplied by 4 is even, the term 4(n^2 + 1) is even , adding 1 to it would make it odd.