Stage:5 Challenge Level:
Show that
\[\sum_{k=0}^n {n\choose k}^2 = {2n \choose n}.\]
Manipulating algebraic expressions/formulae. Binomial Theorem. Visualising. Identities. Creating expressions/formulae. Generalising. Combinatorics. Factors and multiples. Number theory. Mathematical reasoning & proof.
Published February 2001.
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