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Math Topics

Intermediate Algebra

Sequences and Series

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Sequences and Recursion Formulas

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Series

**Mini Lecture**

Expand and simplify.

\(\displaystyle\sum_{i=1}^{4}(2t+4)\)

\(\displaystyle\sum_{i=3}^{6}(-2)^i\)

\(\displaystyle\sum_{i=3}^{6}(x+i)^i\)

Write with summation notation.

\(\displaystyle\frac{3}{4}+\displaystyle\frac{4}{5}+\displaystyle\frac{5}{6}+\displaystyle\frac{6}{7}+\displaystyle\frac{7}{8}\)

\(4+8+16+32+64\)

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Arithmetic Sequences

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Geometric Sequences

**Mini Lecture**

Is the sequence geometric?

\(1, 5, 25, 125, \ldots\)

\(\displaystyle\frac{1}{2}, \displaystyle\frac{1}{6}, \displaystyle\frac{1}{18}, \displaystyle\frac{1}{54}, \ldots\)

If \(a_1=4\) and \(r=3\), find \(a_n, a_{20},\) and \(S_{20}\)

Find \(a_{10}\) and \(S_{10}\) for \(\sqrt{2}, 2, 2\sqrt{2}, \ldots\) \(\displaystyle\frac{1}{2}+\displaystyle\frac{1}{4}+\displaystyle\frac{1}{8}+\ldots=\)?

Show that \(0.444\ldots=\displaystyle\frac{1}{9}\)