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Math Help - Finding Taylor's formula

  1. #1
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    Finding Taylor's formula

    What's the Taylor's series of (a^2+\epsilon)^{\frac{1}{n}}? Using this expansion, what's the value of (.98)^{\frac{1}{3}} accurate to 3 figures beyond the decimal point?

    I tried expanding the series for x^{\frac{2}{n} in powers of \epsilon at x=1 but my answer seems to be off by .6% with the first 3 terms and appears to get worse when I added more.
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  2. #2
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    You should use the Binomial Expansion...
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  3. #3
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    I could, but I want to try using Taylor's series to get a hang of it.
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    Which is your independent variable?
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  5. #5
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    a. I compared the terms in binomial expansion with my version of Taylor's series for x^{\frac{2}{n}} in powers of \epsilon when x=1 and there appears to be a descrepancy in the coefficients. FYI, the answer through binomial expansion is close to the one I got with a calculator.
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  6. #6
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    ok. now the coefficients seems to match if I get a Taylor's series of x^{\frac{1}{n} instead. what gives?
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  7. #7
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    ok. seems I got thrown off by a^2. should have started with f(x)=(x+\epsilon)^{\frac{1}{n}}; x=a^2 and expanded x^{\frac{1}{n}}.
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