Stuck On Mathematical Induction

A

agnes1999

New member
Joined
Feb 15, 2021
Messages
6
Can anyone assist me in solving this? Thanks!

The first few powers of 9 are
= 1,
= 9,
= 81,
= 729. Prove by strong induction that
ends in 1 (unit digits = 1) if n is even and ends in 9 if n is odd.
 
agnes1999 said:
Can anyone assist me in solving this? Thanks!

The first few powers of 9 are
= 1,
= 9,
= 81,
= 729. Prove by strong induction that
ends in 1 (unit digits = 1) if n is even and ends in 9 if n is odd.
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Hey!
I understand understand the question and how to go about the cases. I don't understand how to go about the basis or inductive step and how do I actually prove the hypothesis to be correct for ALL values of n.

I just cannot prove that any results would end with 1 or 9.
 
Why strong induction, when it is easily shown by weak induction?
 
This is a nice problem. I truly hope that you follow our posting guideline so that we can offer some help as I want to see how you plan on writing up this proof.
 
agnes1999 said:
I understand the question and how to go about the cases. I don't understand how to go about the basis or inductive step and how do I actually prove the hypothesis to be correct for ALL values of n.

I just cannot prove that any results would end with 1 or 9.
Click to expand...
It will help us help you if you show the actual work you've done so far, rather than just describing it in general.

I don't know what it means to "understand how to go about the cases", but not "understand how to go about the basis". If you can at least state what you think the basis or base case is, or might be, we can work with that.

I see two ways you might start. One is to work separately with even and odd exponents, making two separate proofs, each using weak induction. Another, perhaps what you are expected to do since they mentioned strong induction (though you can use that even when you don't really need it), is to take two base cases (n=1 and n=2, or n=0 and n=1, according to whether you assume n is supposed to be a positive or non-negative integer). But whatever you choose to start with, we can help you along that path, if you show us what it is.
 
You must log in or register to reply here.
Top