Question
Find the Taylor series for the functions defined as follows. Give the interval of convergence for each series.$$f(x)=\ln \left(1-5 x^{2}\right)$$
Step 1
Step 1: We know that the Taylor series for $\ln(1+x)$ is given by $$\ln(1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \cdots = \sum_{n=1}^{\infty} \frac{(-1)^{n+1}x^n}{n}$$ This series converges for $-1 < x \leq 1$. Show more…
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