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Pascal's Triangle and Binomial Theorem




 
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A Formula for Pascal's Triangle
Well ... "A formula" is not quite the right phrase here, but I will show you in this video how to write down a formula for the 87-th entry of the 198-th row of Pascal's triangle (or any other entry of your choosing) in less than two seconds! And once you see where these entries are coming from, you are all set to understand the binomial theorem. (It's another video!)
The Binomial Theorem
Why is expanding a binomial of the form (x + y)n connected with the n-th row of Pascal's triangle? (For example, the coefficients that appear when expanding (x + y)4 are 1, 4, 6, 4,1 and these represent the fourth row of the triangle.) In this video we explain the connection and show how to have fun and prove mysterious properties of the triangle that you can invent for yourself!
WARNING: This video does rely on having seen the "A Formula for Pascal's Triangle" video just so you know what the entries of Pascal's triangle actually count.



Pascal's Triangle and the Binomial Coefficients


 

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