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Math Help - Taylor series

  1. #1
    dft
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    Taylor series

    hi
    i need help with finding Taylor series for f(z)=1/(4-5z) at z=i

    thx
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  2. #2
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    Quote Originally Posted by dft View Post
    hi
    i need help with finding Taylor series for f(z)=1/(4-5z) at z=i

    thx
    The simplest way to do that is to set z= u+ i so that u= z- i. Then the f(u)= 1/(4- 5(u+ i))= 1/(4- 5i- 5u) or, dividing numerator and denominator by 4- 5i, this is \frac{\frac{1}{4-5i}}{1- \frac{5}{4-5i}u} and recall that \frac{a}{1- r} is the sum of the geometric series \sum_{n=0}^\infty ar^n.
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  3. #3
    dft
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    thanks
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