Question

The sum of two consecutive integers is at most ____. Enter your answer in the box.

a) -1
b) 0
c) 1
d) 2

Answer 1

The sum of two consecutive integers is always one more than twice the smaller integer. Therefore, the maximum sum is infinite.

Step-by-step explanation:

The sum of two consecutive integers can be found by adding the two integers together. Since the integers are consecutive, they have a difference of 1. So, if we let the smaller integer be x, the larger integer would be x+1. Therefore,
The sum of the two consecutive integers is x + (x+1) = 2x + 1.

So, the sum of two consecutive integers is always one more than twice the smaller integer.

To find the maximum value of the sum, we want to maximize the smaller integer. Since there is no limit given in the question, the answer would be infinite. Therefore, none of the options (a) -1, (b) 0, (c) 1, or (d) 2 is correct.