# 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

**odd**

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

**ODD** (where p is a natural number)

now since all three,