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    hi,

    I cant find my notes on binomeal expsansions and have searched google buy cant make head or tail of it

    could someone do these two so I can get the jist

    thanks

    y = (1 + 3x)^0.5

    y = (2 - x)^-3

    thanks alot
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    (Original post by tom_austin)
    hi,

    I cant find my notes on binomeal expsansions and have searched google buy cant make head or tail of it

    could someone do these two so I can get the jist

    thanks

    y = (1 + 3x)^0.5

    y = (2 - x)^-3

    thanks alot
    (1+x)^n=1+nx+[n(n-1)/2]x^2+[n(n-1)(n-2)/6]x^3+[n(n-1)(n-2)(n-3)/24]x^4+...........+[n(n-1)(n-2)....(n-r+1)/r!]x^r.

    I don't know what you mean by 'do these two' as the series are infinite.
    (1+3x)^0.5=1+(0.5)(3x)+[(0.5)(-0.5)/2](3x)^2+........
    (2-x)^-3=[2^-3][1-0.5x]^-3=(1/8)[1+(-3)(-0.5x)+(-3)(-4)(-0.5x)^2/2+....]
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    (Original post by Gaz031)
    (1+x)^n=1+nx+[n(n-1)/2]x^2+[n(n-1)(n-2)/6]x^3+[n(n-1)(n-2)(n-3)/24]x^4+...........+[n(n-1)(n-2)....(n-r+1)/r!]x^r.

    I don't know what you mean by 'do these two' as the series are infinite.
    (1+3x)^0.5=1+(0.5)(3x)+[(0.5)(-0.5)/2](3x)^2+........
    (2-x)^-3=[2^-3][1-0.5x]^-3=(1/8)[1+(-3)(-0.5x)+(-3)(-4)(-0.5x)^2/2+....]
    cheers...ill try it on some exam questions
    thanks
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    P5... isn't that a further module? This looks like the same thing as in C4.
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    (Original post by ljfrugn)
    P5... isn't that a further module? This looks like the same thing as in C4.
    This isn't P5. It was probably a typo or an abbreviation for something else.
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    P5 Aqa
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    It is Pure 5 on the old (before it became 'core') AQA syllabus for pure maths and stats. We do P1, 2, 4, 5 and S1, 4
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    (Original post by kpg)
    It is Pure 5 on the old (before it became 'core') AQA syllabus for pure maths and stats. We do P1, 2, 4, 5 and S1, 4
    ye...were doing P1,P2,P4,P5 & M1,M2
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    (Original post by Gaz031)
    (1+x)^n=1+nx+[n(n-1)/2]x^2+[n(n-1)(n-2)/6]x^3+[n(n-1)(n-2)(n-3)/24]x^4+...........+[n(n-1)(n-2)....(n-r+1)/r!]x^r.

    I don't know what you mean by 'do these two' as the series are infinite.
    (1+3x)^0.5=1+(0.5)(3x)+[(0.5)(-0.5)/2](3x)^2+........
    (2-x)^-3=[2^-3][1-0.5x]^-3=(1/8)[1+(-3)(-0.5x)+(-3)(-4)(-0.5x)^2/2+....]
    The expansion

    (1+x)^a = 1 + ax + a(a-1)/2! x^2 + a(a-1)(a-2)/3! x^3 + ....

    is still called the binomial expansion even when a isn't a natural number.

    As you've said, in those cases it doesn't terminate and converges only when |x|<1
 
 
 
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