Proof by induction for (n+3)^2 <= 2^(n+3)

[marc.foschi]

I've to proof by induction the following:

(n+3)^2 <= 2^(n+3)

Please detail the steps.


Thanks
Regards

 

[Deleted member 4993]

I've to proof by induction the following:

(n+3)^2 <= 2^(n+3)

Please detail the steps.


Thanks
Regards

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[ksdhart2]

I'd also note that when using proof by induction, you must always specify the value(s) of n for which the proof is valid. Without such a declaration, the default assumption is that it is valid for all n, which is not the case here. As just one example of a value that won't work, consider the case when n = -4:

(-4 + 3)^2 <= 2^(-4 + 3)
(-1)^2 <= 2^(-1)
1 <= 1/2
False!

 

[stapel]

I've to proof by induction the following:

(n+3)^2 <= 2^(n+3)

Please detail the steps.

Sorry, but this isn't one of those "cheetz" sites. We need to see your efforts, first. For further information, please re-read the "Read Before Posting" announcement.

For general instruction on how to do induction proofs, please try here. Once you have learned the basic terms and techniques (the "steps", as you called them), please attempt the exercise. If you get stuck, you can then reply with the rest of the exercise (such as the limit on "n" -- are we supposed to assume "for n a natural number"? etc) and a clear listing of your thoughts and efforts so far.

Thank you!