Solution Bank Sequences and Series Target A
Answers to the Practice Problems are below in random order.
\(\begin{align}&a_n=14-3n\ & \ \ &\sum\limits_{n=1}^{16} \frac{1}{n}\ & \ \ &4, \frac{7}{8}, \frac{10}{27}, \frac{13}{64}, \frac{16}{125}, \frac{19}{216}\\\\
&\text{Converging to 2}\ & \ \ &\sum\limits_{n=1}^{\infty} 16-14n\ & \ \ &2, 1, \frac{2}{3}, \frac{1}{2}, \frac{2}{5}, \frac{1}{3}\\\\&32\ & \ \ &\sum\limits_{n=1}^{9} 13n\ & \ \ &1,5,21,73,233,717\\\\
&30\ & \ \ &\sum\limits_{n=1}^{\infty} \frac{3}{n^3}\ & \ \ &5,8,11,14,17,20\\\\
&e\ & \ \ &\frac{205}{144}\ & \ \ &-6, -10, -17, -30, -55, -104\\\\
&x=\frac{7}{36}\ & \ \ &(5,0)\ & \ \ &\frac{1}{3}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{5}{7}, \frac{3}{4}\\\\
&748\ & \ \ &\frac{511}{256}\ & \ \ &\text{Does not converge}\\\\
&a_n=5\ & \ \ &a_n=n^2+1\end{align}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&a_n=14-3n\ & \ \ &\sum\limits_{n=1}^{16} \frac{1}{n}\ & \ \ &4, \frac{7}{8}, \frac{10}{27}, \frac{13}{64}, \frac{16}{125}, \frac{19}{216}\\\\
&\text{Converging to 2}\ & \ \ &\sum\limits_{n=1}^{\infty} 16-14n\ & \ \ &2, 1, \frac{2}{3}, \frac{1}{2}, \frac{2}{5}, \frac{1}{3}\\\\&32\ & \ \ &\sum\limits_{n=1}^{9} 13n\ & \ \ &1,5,21,73,233,717\\\\
&30\ & \ \ &\sum\limits_{n=1}^{\infty} \frac{3}{n^3}\ & \ \ &5,8,11,14,17,20\\\\
&e\ & \ \ &\frac{205}{144}\ & \ \ &-6, -10, -17, -30, -55, -104\\\\
&x=\frac{7}{36}\ & \ \ &(5,0)\ & \ \ &\frac{1}{3}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{5}{7}, \frac{3}{4}\\\\
&748\ & \ \ &\frac{511}{256}\ & \ \ &\text{Does not converge}\\\\
&a_n=5\ & \ \ &a_n=n^2+1\end{align}\)