SOLUTION: what name is given to all the numbers that can be expressed as the sum of two consecutive numbers?

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Question 366143: what name is given to all the numbers that can be expressed as the sum of two consecutive numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let n = first number (which is an integer)

So n%2B1 is the next consecutive number.


Now add up the two numbers to get n%2B%28n%2B1%29=%28n%2Bn%29%2B1=2n%2B1


Since n is an integer, 2n is even (since 2 is a factor). So 2n%2B1 is odd.


So any odd number can be expressed as the sum of two consecutive numbers.


So to answer the question "what name is given to all the numbers that can be expressed as the sum of two consecutive numbers?", the answer is the set of odd integers.