# 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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