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(a) Compute the sums of the squares of Rows 1-4 of Pascal's Triangle. That is, compute:

Do these sums appear anywhere else in Pascal's Triangle?

(b) Guess at an identity based on your observations from part (a). Your identity should be of the form

$$\binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 = \text{ something}.$$

(You have to figure out what "something" is.) Test your identity for  using your results from part (a).

(c) Prove your identity using a committee-forming argument.

(d) Prove your identity using a block-walking argument.

 Aug 16, 2019
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 Sep 20, 2019

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