Question

6n −1 is divisibleby 5, for n >0 using mathematical induction

Answer 1

6n - 1 is divisible by 5 for n = 1
HOWEVER if n = 2
12 - 1 = 11
which is not divisible by 5 in my world.
Neither is 17

Answer 2

I suspect a typo in the problem statement but have not been able to guess what it is.

Answer 3

To prove that 6n − 1 is divisible by 5 for n > 0 using mathematical induction, we will follow these steps:

Step 1: Base case
For n = 1, we have 6n - 1 = 6(1) - 1 = 5, which is divisible by 5.

Step 2: Inductive hypothesis
Assume that 6k - 1 is divisible by 5 for some positive integer k > 0. This is our inductive hypothesis.

Step 3: Inductive step
We need to prove that 6(k + 1) - 1 is divisible by 5 based on our inductive hypothesis.

Simplifying 6(k + 1) - 1, we get:
6k + 6 - 1 = 6k + 5

Since we assumed that 6k - 1 is divisible by 5, we can write it as 5m for some positive integer m.

Therefore, 6k + 5 = 5m + 5 = 5(m + 1), which is divisible by 5.

Step 4: Conclusion
By mathematical induction, we have shown that if 6k - 1 is divisible by 5 for some positive integer k > 0, then 6(k + 1) - 1 is divisible by 5 as well.

Therefore, 6n - 1 is divisible by 5 for n > 0.

Answer 4

Apologies for the mistake. It appears that the statement "6n - 1 is divisible by 5 for n > 0" is incorrect. In fact, if we substitute n = 2, we get 6n - 1 = 6(2) - 1 = 11, which is not divisible by 5. Therefore, the statement is false and cannot be proven using mathematical induction. Thank you for pointing out the error.

Answer 5

Apologies for any confusion caused. It seems that there might be a typographical error in the problem statement. If you can provide any additional information or context, I would be happy to assist you in resolving the issue.