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binomial expansion
chapter 8 - binomial expansion
Term | Definition |
---|---|
Pascal’s triangle | a “sequence” formed by adding the adjacent numbers of the numbers above (the left/right most numbers of a row is always 1) |
pascal’s triangle coefficients | the n’th row (assuming you start from 0) gives the coefficients of (a+b)^n |
factorial definition | n! := n*(n-1)*(n-2)*…*2*1 0! = 1 |
the choose function | nCr = n choose r := n!/(r!(n-r)!) |
binomial expansion | (a+b)^n = a^n + (nC1)a^(n-1)b + (nC2)a^(n-2)b^2… (nCn)b^n, where n is a natural number |
the general term of an expansion | (nCr)a^(n-r)b^r |
binomial estimation | as long as the expansion converges, x^n can be used to approximate functions or values. Larger powers are often ignored due to their “lack of significance” |