Difference between revisions of "User:Saul/algebra"
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== Binomial Theorem == | == Binomial Theorem == | ||
− | <big>'''(a + b)<sup>n</sup> = <sub>k=0</sub>Σ<sup>n</sup>((n choose k)a<sup>k</sup>b<sup>n-k</sup>)'''</big> | + | <big>'''(a + b)<sup>n</sup> = <sub>k=0</sub>Σ<sup>n</sup> ((n choose k) a<sup>k</sup>b<sup>n-k</sup>)'''</big> |
=== Approximation Using Binomial === | === Approximation Using Binomial === |
Revision as of 03:37, 25 September 2019
Contents
Combinations and Permutations
Permutations/Pick
A permutation is a sequence where the order does matter.
This is often notated by n pick r where n is the data set - say 40 lotto balls and r is the selection count - say 8 balls.
The general formulae for permutations is:
P = n! / (n-k)!
Combinations/Choose
A combination is a sequence where the order does NOT matter.
This is often notated by n choose r - n and r mean the same thing as in pick.
The general formulae for combinations is:
C = n! / ((n-k)!k!)
Also note that:
n choose k is the same as n choose (n - k)
Binomial Theorem
(a + b)n = k=0Σn ((n choose k) akbn-k)
Approximation Using Binomial
Calculating a number to the power of another can be approximated by the following formulae:
(1 + x)n = 1 + nx + (n(n-1)x2)/2! + (n(n-1)(n-2)x3)/3! + (n(n-1)(n-2)(n-3)x4)/4! ...
Note: This is unending so the more steps you take the more accurate the number will be, however usually 3-4 steps is enough.