
### Instruction: help me answer this question Is n (n + 1) (n + 5) a multiple of 3 for all natural numbers, i.e., n?, think step by step
### Assistant: This can be proved using the principle of mathematical induction. For n=1, n (n + 1) (n + 5) = 12, which is divisible by 3. Assuming P (k) to be true for some positive integer k, it can be shown that P (k + 1) is also true, hence P (n) is true for all natural numbers, i.e., n. , The answer is Yes, n (n + 1) (n + 5) is a multiple of 3 for all natural numbers.
