Stage: 5 Challenge Level: 
Show that
\[\sum_{k=0}^n {n\choose k}^2 = {2n \choose n}.\]
Generalising. Binomial Theorem. Manipulating algebraic expressions/formulae. Identities. Stage 5 - Reviewed 2012. Dynamical systems. Inequality/inequalities. Patterned numbers. Mathematical reasoning & proof. Number theory.
Published February 2001.
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