(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello,

This expression was derived from a polygon word problem and I need to find a closed form for it with repeated substitution (I think).

T(k, n) = T(k, n-1) + (k-2)(n-1) + 1

2. Relevant equations

3. The attempt at a solution

Get a pattern like:

= T(k, n-2) + (k - 2)(2n - 3) - 2 subs.

= T(k, n-3) + (k - 2)(3n - 6) - 3 subs.

= T(k, n-4) + (k - 2)(4n - 10) -4 subs.

.

.

.

I'm not sure how to express the 1, 3, 6, 10 sequence in terms of number of substitutions.

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# How to get the closed form of this recurrence?

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