How can we prove using mathematical induction that #n^2+n+1# is an odd number if n is a natural number?
1 Answer
See Explanation.
or try again yourself keeping in mind that : -
Any even number can be represented as 2t and any odd number can be represented as 2t+1 where t is also a natural number
Explanation:
Assuming you know the general algorithm of Principle of mathematical induction;
1 . Checking if the statement is true for
2 . Assuming statement is true for some natural number
i.e.
i.e.
[any even number can be represented as 2t and any odd number can be represented as 2t+1 where t is also a natural number]
3 . To prove that statement is true for natural number next to
now since all three,