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The first three terms of a series are given by:
\n\\(\\var{a} + \\simplify{{a}*{r}} + \\simplify{{a}*{r}^2}\\,+ \\, ...........\\)
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\n\\(S_\\var{n}=\\) [[0]]
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\nThs first term is \\(a\\) and the common ratio is \\(r\\).
\nThe formula for the sum of the first \\(n\\) terms of the series is given by: \\(S_n=\\frac{a(1-r^{n})}{1-r}\\)
\nIn this example \\(a=\\var{a}\\), \\(r = \\frac{\\simplify{{a}*{r}}}{\\var{a}}=\\var{r}\\) and \\(n = \\var{n}\\)
\n\\(S_\\var{n}=\\frac{\\var{a}(1-(\\var{r})^{\\var{n}})}{1-\\var{r}}\\)
\n\\(S_\\var{n}=\\frac{\\var{a}*(\\simplify{1-{r}^{n}})}{\\simplify{1-{r}}}\\)
\n\\(S_\\var{n}=\\frac{\\simplify{{a}*(1-{r}^{n})}}{\\simplify{1-{r}}}\\)
\n\\(S_\\var{n}=\\var{s}\\)
", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}