Question

Prove that the sum of any 5 consecutive natural number is divisible by 5​

Answer 1

2 + 3 + 4 + 5 + 6 = 20

20/5 = 4

Answer 2

Explanation:

Theorem: If n is the sum of five consecutive integers, then n is divisible by 5. Conversely, if n is divisible by 5, then n is the sum of five consecutive integers. In particular, this gives n = 5m + 10 = 5(m + 2) and, since m + 2 is an integer, this shows n is divisible by 5.