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Proof by induction is a proof made by first assuming that a statement is true for a general case (i.e. when EQN:n=k ), then proving that it still holds true for the next case (i.e. when EQN:n=k+1 ) and then proving that it is true for the first (base) case; if the statement /does/ hold for /both/ the base case /and/ the inductive step ( EQN:n=k+1 ), then, by induction, the statement must be true. !! METHOD To prove that something is true for all integers EQN:n{\ge}r : * assume that it is true for EQN:n=k * prove that it remains true for EQN:n=k+1 * prove that it is true for EQN:n=r. !! Examples It would be nice to have some small, clean examples here. Not too many, not too much.