# What is the sum of any two-odd number?

Answer

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Hint: Here we can add any two-odd numbers and prove that the answer will be an even number, but to achieve that we have to express an odd number in its general form then add two numbers in general form and get the sum.

“Complete step-by-step answer:”

As you know odd number is in the form of $\left( {2n - 1} \right)$ or $\left( {2n + 1} \right)$ (where n = 1, 2, 3…..)

$ \Rightarrow $sum of odd numbers is

$ \Rightarrow \left( {2n - 1} \right) + \left( {2n + 1} \right)$

$ \Rightarrow 2n - 1 + 2n + 1 = 4n$

Now as you know multiplication of 4 in any number is an even number

Therefore, the sum of any odd numbers is an even number.

NOTE: whenever we face such a problem the key concept is that we have to remember the general term of an odd number.

“Complete step-by-step answer:”

As you know odd number is in the form of $\left( {2n - 1} \right)$ or $\left( {2n + 1} \right)$ (where n = 1, 2, 3…..)

$ \Rightarrow $sum of odd numbers is

$ \Rightarrow \left( {2n - 1} \right) + \left( {2n + 1} \right)$

$ \Rightarrow 2n - 1 + 2n + 1 = 4n$

Now as you know multiplication of 4 in any number is an even number

Therefore, the sum of any odd numbers is an even number.

NOTE: whenever we face such a problem the key concept is that we have to remember the general term of an odd number.

Last updated date: 01st Jun 2023

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