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Notes
Questions
Find the infinite geometric series
\(\textbf{1)}\) \(a_1=8 \,\, r=.75 \)
\(\textbf{2)}\) \(a_1=.75 \,\, r=8 \)
\(\textbf{3)}\) \(\displaystyle\frac{1}{2}+\displaystyle\frac{1}{4}+\displaystyle\frac{1}{8}+\displaystyle\frac{1}{16}+ \cdots\)
\(\textbf{4)}\) \(\displaystyle\frac{1}{2}-\displaystyle\frac{1}{4}+\displaystyle\frac{1}{8}-\displaystyle\frac{1}{16}+ \cdots\)
\(\textbf{5)}\) \(\displaystyle\frac{1}{20}-\displaystyle\frac{1}{10}+\displaystyle\frac{1}{5}-\displaystyle\frac{2}{5}+ \cdots\)
\(\textbf{6)}\) \( \displaystyle \sum_{i=1}^{\infty} 4\left( \frac{1}{3} \right)^{i-1} \)
See Related Pages
\(\bullet\text{ Arithmetic Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 + d(n-1)\)
\(\bullet\text{ Geometric Sequences}\)
\(\,\,\,\,\,\,\,a_n=a_1 \cdot r^{(n-1)}…\)
\(\bullet\text{ Arithmetic Series}\)
\(\,\,\,\,\,\,\,s_n=\frac{n}{2}(a_1+a_n)…\)
\(\bullet\text{ Geometric Series}\)
\(\,\,\,\,\,\,\,s_n=a_1 \frac{1-r^n}{1-r}…\)
\(\bullet\text{ Summation Notation}\)
\(\,\,\,\,\,\,\, \displaystyle \sum_{i=4}^{9} 3i-5 …\)
\(\bullet\text{ Recursive Sequences}\)
\(\,\,\,\,\,\,\, a_{1}=2, \, a_{n+1}=a_{n}+3…\)
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