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1205 Binomial Expansion Theorem
3183 days ago by MATH4R2012
for n in range(5): expand((x+1)^n)
for n in range(10): factorial(n)
#p851(45) (1/4+3/4)^5
def combo(n,r): return factorial(n)/factorial(r)/factorial(n-r) combo(5,3)
(100*combo(5,0)*(1/4)^5*(3/4)^0).n()
for r in range(5): show((100*combo(5,r)*(1/4)^(5-r)*(3/4)^r).n())
#10) 60 C 20 combo(60,20)
#20) (x^2-y^2)^6 var('y') expand((x^2-y^2)^6)
combo(6,0)*(x^2)^6*(-y^2)^0
combo(6,1)*(x^2)^5*(-y^2)^1
combo(6,2)*(x^2)^4*(-y^2)^2
combo(6,3)*(x^2)^3*(-y^2)^3
combo(6,4)*(x^2)^2*(-y^2)^4
combo(6,5)*(x^2)^1*(-y^2)^5
combo(6,6)*(x^2)^0*(-y^2)^6
for r in range(7): combo(6,r)
#30) expand((2*x-3)^9)
combo(9,7)*(2*x)^2*(-3)^7
combo(9,5)*(2*x)^4*(-3)^5