Question: (1) Consider r+2 + +...+ r ) + ( ) = ( * (a) Draw Pascal's triangle and indicate what this identity is

(1) Consider r+2 + +...+ r " ) + ( " ) = (" * (a) Draw Pascal's triangle and indicate what this identity is saying on the triangle when r = 2 and n = 5. (b) Prove the identity using induction on n (where r is fixed but arbitrary). (c) Prove the identity combinatorially (Hint: consider the largest element of the (r+ 1) subset of [n + 1])

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