Taylor polynomials question

**natashabu** · December 10th 2008, 05:24 PM

It's probably not that hard of a question but I don't really understand taylor polynomials.. Thanks a lot if you can explain it to me

the question is:
determine the sum of -4(1/5) + 4(1/5)^2 - 4(1/5)^3 + 4(1/5)^4 - ...

**o_O** · December 10th 2008, 05:32 PM

Let's write it as: ${\color{red}4} {\color{blue}\left(-\tfrac{1}{5}\right)} + {\color{red}4}{\color{blue}\left(-\tfrac{1}{5}\right)}^2 + {\color{red}4}{\color{blue}\left(-\tfrac{1}{5}\right)}^3 + {\color{red}4}{\color{blue}\left(-\tfrac{1}{5}\right)}^4 + \cdots$

Geometric series should ring a bell.

Recall: $\sum_{n=0}^{\infty} {\color{red}a}{\color{blue}r}^{n-1} = {\color{red}a} + {\color{red}a}{\color{blue}r} + {\color{red}a}{\color{blue}r}^2 + {\color{red}a}{\color{blue}r}^3 + \cdots = \frac{{\color{red}a}}{1-{\color{blue}r}} \quad \text{if } |{\color{blue}r}| < 1$

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