Monday, May 9, 2016

discrete mathematics - Induction Proof The sum of the first n odd squares

I am just learning about induction proofs. So far I am only familiar with induction equality proofs, and inequality proofs. Such as, for example, prove the sum of the powers of 2 = $2^{n+1} - 1$...



I am confused on the following proof:
The sum of the first n odd squares is $\frac 43 n^3 - \frac 13n$



How do I start this proof? it looks like only one statement with nothing to compare it to. I was thinking maybe I would represent the sum of the first n odd squares as the formula $(2n - 1)^2$ and then set the proof up as
$(2n - 1)^2 = \frac 43 n^3 - \frac 13n$




so it looks more like the form I am used to. Is this correct? Am I missing a small nuance of importance? Thanks for any and all help.

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...