Stephen M. answered • 12/29/16

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Naval Academy Grad for Math and Science Tutoring

That's an important first step. You've proven that it works for n = 1. In order to use induction, we need to prove that if it's true for n-1, then it must be true for n. Let S

_{n}be the sum through n. Then,S

_{n}= S_{n-1}+ 2n^{2}- 4n + 3 (based on the definition of our sum)Sn = (n-1)/3 * (2(n-1)

^{2}- 3(n-1) + 4) + 2n^{2}- 4n + 3 (based on substituting in our formula for S_{n-1})Now, all you need to do is multiply out and simplify this expression and demonstrate that it comes out to

n/3(2n

^{2}- 3n + 4)If you need additional help with that, feel free to let me know.

Mark M.

12/29/16