Chapter 8.3, Problem 15P

a. If you add 2 consecutive counting numbers (such as 47, 48), will the resulting sum always, sometimes, or never be divisible by 2? Explain why your answer is true.

b. If you add 3 consecutive counting numbers (such as 47, 48, 49), will the resulting sum always, sometimes, or never be divisible by 3? Explain why your answer is true.

c. If you add 4 consecutive counting numbers (such as 47, 48, 49, 50), will the resulting sum always, sometimes, or never be divisible by 4? Explain why your answer is true.

d. If you add 5 consecutive counting numbers (such as 47, 48, 49, 50, 51), will the resulting sum always, sometimes, or never be divisible by 5? Explain why your answer is true.

e. If you add N consecutive counting numbers, will the resulting sum always, sometimes, or never be divisible by N? Explain why your answer is true.