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# Tag Archives: identity

## Combinatorial proofs

Continuing from a previous post, we found that if we begin with th powers of consecutive integers and then repeatedly take successive differences, it seems like we always end up with the factorial of , that is, . We then … Continue reading

Posted in combinatorics, pictures, proof
Tagged binomial coefficients, combinatorial proof, identity
12 Comments

## Cassini’s identity

My previous post asked you to take any Fibonacci number, square it, and also multiply the two adjacent Fibonacci numbers, and see if a pattern emerged. Here’s a table I made for the first 6 Fibonacci numbers: (Hmm, the numbers … Continue reading