Proof by Induction: Solving Algebraic Exercises

[woundedtiger4]

Hi everyone,
I am trying to learn proof by induction method from http://en.m.wikibooks.org/wiki/Algebra/Proofs/Exercises
And I have tried to solve the second problem attached with this post. It will be great if someone can tell me if I am wrong anywhere and then guide me.

Thanks in advance.

 

[Mark44]

Hi everyone,
I am trying to learn proof by induction method from http://en.m.wikibooks.org/wiki/Algebra/Proofs/Exercises
And I have tried to solve the second problem attached with this post. It will be great if someone can tell me if I am wrong anywhere and then guide me.

Thanks in advance.

The line quoted below is wrong.
"It follows that (k + 1)! > 2^{k + 1}"
This is precisely what you need to show! You can't just wave your arms and say that "it follows that ..." without showing it.

To show this, note that (k + 1)! = (k + 1)k!. Use your induction hypothesis (i.e., that k! > 2^k) to finish the proof.

BTW, your thread should have been posted in the Homework & Coursework section, not in the technical math sections (especially not in the Linear and Abstract Algebra section. I am moving your thread.