Monday, June 1, 2009

Induction

Induction: a technique for proving a statement, theorum, or formula.

Prove that Sn = 1+3+5+7....+(2n-1)=n²

step 1. prove that its true when n=1
S₁= 1= n²
1= 1² a
step 2. assuming that its true at n, show that its true at n+1
Sn+1= 1+3+5+...+(2n-1) + [2(n+1)-1] = (n+1)²
replace 1+3+5+...+(2n-1) with n² because you assume that it is true at n.
Sn+1= n²+ (2n+2-1) = n²+2n+1
Sn+1= n²+2n+1 = n²+2n+1 a

Practice Problems:

1. Prove the following statement is true for all positive integers of n.


2. Prove the following statement is true for all positive integers of n.



3. Prove the following statement is true for all positive integers of n.





4. Prove the following statement is true for all positive integers of n.


5. Prove the following statement is true for all positive integers of n.





6. Prove the following statement is true for all positive integers of n.



7. Prove the following statement is true for all positive integers of n.





8. Prove the following statement is true for all positive integers of n.



9. Prove the following statement is true for all positive integers of n.




10. Prove the following statement is true for all positive integers of n.



2 comments:

Kate Nowak said...

It's spelled "theorem" :-)

Kate Nowak said...

I find the beginning section a bit hard to follow/read. Try different sized fonts and play with the spacing. Ask some other people to try to read it and give you feedback.

You can use the SITMO editor for a multi-line solution, or you can ask Julia and Kelsey about using MathType. I'd like to see at least a couple of your practice problems with a proof worked out.