Tennis Ball Pyramid

Algebra Level 2

We build triangle pyramids from \(N\) tennis balls, each with number of layers \(n=\) 1, 2, 3, or ... (The base of the pyramid is also a triangle.) The trivial pyramid with a single layer consists of a single ball. Two layers require four balls, while the three-layer pyramid requires ten balls.

What is the number \(N\) of balls required for the pyramid with \(n = 100\) layers?

Hint: Find a polynomial \( N (n) \) that describes the number of balls as a function of the edge length \( n \).

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