(See Steps) By considering S_n=1+x+x^2+•s+x^n, or otherwise, show that for |x|<1 (1)/(1-x)=1+x+x^2+x^3+x^4+x^5+•s Use this result to find the

Question: By considering $S_{n}=1+x+x^{2}+\cdots+x^{n}$, or otherwise, show that for $|x|<1$

\[\frac{1}{1-x}=1+x+x^{2}+x^{3}+x^{4}+x^{5}+\cdots\]

Use this result to find the Taylor series of the functions below and indicate the values of $x$ for which the corresponding series converges:

\[\text { (a) } \frac{1}{2-x}, \quad \text { (b) } \frac{x}{1+x-2 x^{2}}, \quad \text { (c) } \log \left(\frac{1+x}{1-x}\right) \text { . }\]

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(See Steps) By considering S_n=1+x+x^2+•s+x^n, or otherwise, show that for |x|<1 (1)/(1-x)=1+x+x^2+x^3+x^4+x^5+•s Use this result to find the

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