How can i find all of the numbers in a certain row of pascals triangle, for this example lets say the 11th row, without having to draw out the entire triangle?
In: Mathematics
/u/IncompetentTaxPayer has the general formula for any row of Pascal’s triangle.
“nChooseK” sometimes written as C(n,k) = n! / ( k! *(n-k)! )
I’ll add some other interesting things here. The triangle also shows the progressive values of 11, 11^2, 11^3, etc. Since the nth row is 11^n which can be written as (x+1)^n where x=10. Kind of fun.
Euler’s Characteristic https://en.wikipedia.org/wiki/Euler_characteristic 2 = VertexCount – EdgeCount + FaceCount can also be extended into higher dimentions by this (x+1)^n method.
Turns out polynomials, especially the simple (x+1)^n is found everywhere.
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