SOLUTION: What other interesting patterns can you find in Pascal's triangle? 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

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Question 158956: What other interesting patterns can you find in Pascal's triangle?
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Answer by Alan3354(21605) About Me  (Show Source):
You can put this solution on YOUR website!
What other interesting patterns can you find in Pascal's triangle?
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
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It's the coefficients of a binomial expansion, ie,
1 (x+1)^0 = 1
1 1 (x+1)^1 = 1x + 1
1 2 1 (x+1)^2 = 1x^2 + 2x + 1
1 3 3 1 (x+1)^3 = 1x^3 + 3x^2 + 3x + 1
1 4 6 4 1 (x+1)^4 = 1x^4 + 4x^3 + 6x^2 + 4x + 1
1 5 10 10 5 1 (x+1)^5 = 1x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1