binomial expansion with rational exponents Watch

doremi
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#1
Report Thread starter 9 years ago
#1
hello

I am asked to use bionomial expnasion in the following expressions

i) x[(1+x^2)^1/2] and ii) x^3/2[1-(e^-x)]

I self study and haven't seen any worked examples for binomial expansions with rational exponents. I am hoping that you will direct me at a link where such examples are available (I am well and trully stuck otherwise) or provide some help with how to tackle the particular examples.
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insparato
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#2
Report 9 years ago
#2
The process when using fractional powers is no different to using the binomial expansion with integers.

 (1 + x)^{n} = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!} x^3 + ..... +

Just pop in n = 1/2.
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doremi
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#3
Report Thread starter 9 years ago
#3
right thanks
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hypnogogia
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#4
Report 8 years ago
#4
can anyone help me understand why, in the above example, |x| must be < 1?
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