sum formula for 1/x^2 + 1/x^2 + 1/x^3 + ...?
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Re: last question - sum formula?
Hello, deemanw!
The sum of an infinite geometric series is: \(\displaystyle \L\,S \;=\;\frac{a}{1 - r}\)
\(\displaystyle \;\;\)where \(\displaystyle a\) is the first term and \(\displaystyle r\) is the common ratio.
We are given a geometric series with: \(\displaystyle \,a\,=\,\frac{1}{x}\) and \(\displaystyle r\,=\,\frac{1}{x}\)
Therefore, the sum is: \(\displaystyle \L\,S\;= \;\frac{\frac{1}{x}}{1\,-\frac{1}{x}} \;= \;\frac{1}{x\,-\,1}\)
Hello, deemanw!
The sum of an infinite geometric series is: \(\displaystyle \L\,S \;=\;\frac{a}{1 - r}\)
\(\displaystyle \;\;\)where \(\displaystyle a\) is the first term and \(\displaystyle r\) is the common ratio.
We are given a geometric series with: \(\displaystyle \,a\,=\,\frac{1}{x}\) and \(\displaystyle r\,=\,\frac{1}{x}\)
Therefore, the sum is: \(\displaystyle \L\,S\;= \;\frac{\frac{1}{x}}{1\,-\frac{1}{x}} \;= \;\frac{1}{x\,-\,1}\)
