Question

Show algebraically that the sum of two consecutive numbers is always odd.

Answer 1

If we add two odd numbers we will definitely get an even number but if we add one odd and one even we get odd numbers only. So add one odd and one even so you get an odd number only.

Answer 2

Answer:

The sum of two consecutive numbers (x and x + 1) will usually be strange (2x + 1).

Step-by-step explanation:

From the above question,

     Let's anticipate the first of the two consecutive numbers is x. Therefore, the subsequent consecutive wide variety would be x + 1.

Consecutive numbers can be positive, negative, or consist of zero. For example, -3, -2, -1, zero are consecutive numbers due to the fact every quantity is one greater than the one earlier than it, and they structure a sequence with a distinction of 1.

Similarly, 6, 7, 8, 9, 10 are consecutive numbers due to the fact every quantity is one greater than the one earlier than it and they structure a sequence with a distinction of 1.

The sum of these two consecutive numbers would be:

                         x + (x + 1)

Simplifying the expression:

                         2x + 1

Since 2x is an even quantity (as it is the product of two and x, and x can be any integer), including 1 to it will constantly end result in an abnormal number.

Therefore,

                The sum of two consecutive numbers (x and x + 1) will usually be strange (2x + 1).

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