What is wrong with the "proof"? Claim: All cats have the same fur Proof: By induction on n, the number of cats. If n = 1, then there is only one cat, so only one fur, so it’s trivially the same fur as itself. Now suppose that the statement is true for k − 1 cats, and we’ll show it holds for k cats. Line the cats up, and consider the first k − 1 cats. By the inductive hypothesis, they must have the same fur. Now consider the last k − 1 cats. Again, they must have the same fur. But the cats in the middle couldn’t have changed fur, so all k cats must have the same fur.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.