5.17 Functions expressed as power series

Functions expressed as power series

Lessons

Notes:
Note *A formula that may be of use when expressing functions into power series:

11r=n=0rn\frac{1}{1-r}=\sum_{n=0}^{\infty}r^n knowing that 1-1 < rr < 11

When finding the interval of convergence, there is no need to check the endpoints. This is because the sum of the geometric series strictly converges only when 1-1 < rr < 11, and not at r=1r=1.

If the function f(x)f(x) has a radius of convergence of RR, then the derivative and the anti-derivative of f(x)f(x) also has a radius of convergence of RR.
  • 1.
    Expressing Functions as Power Series
    Express the following functions as power series, and then find the interval of convergence:
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Functions expressed as power series

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