RE: The Mathematical Proof Thread
January 28, 2017 at 10:24 am
(This post was last modified: January 28, 2017 at 10:26 am by Kernel Sohcahtoa.)
Hello AF members. When I first made this thread, I had intended it to be one of those threads where people could post endlessly even if there were a long intermission between posts such as this post. Hence, I want to apologize to the staff if I'm breaking the rules by posting this.
With that said, I didn't recall seeing many induction proofs here, so I thought I'd post one for any member who is curious about induction, especially for the younger members (high school) who are getting interested in mathematics. Here it is:
Prove that 1^2+2^2+…+ (n-1)^2 < n^3/3 < 1^2+2^2+…+ n^2 is true for all positive integers n.
Hint: use mathematical induction.
Background on Mathematical Induction
Proof
With that said, I didn't recall seeing many induction proofs here, so I thought I'd post one for any member who is curious about induction, especially for the younger members (high school) who are getting interested in mathematics. Here it is:
Prove that 1^2+2^2+…+ (n-1)^2 < n^3/3 < 1^2+2^2+…+ n^2 is true for all positive integers n.
Hint: use mathematical induction.
Background on Mathematical Induction
Proof