Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for and .
i) The Maclaurin series
ii) The radius of convergence of
i) For a power series , there is a positive number such that the series converges if and diverges if , this number is called the radius of convergence and the series is centred at .
ii) The Maclaurin series expansion for .
iii) The ratio test:
If then the series is absolutely convergent, and
if then the series diverges.
It is given that,
It can be written as, using the rules of logarithm,
Replace by in the Maclaurin series expansion for .
This is the Maclaurin series expansion for
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