Section 1
Sigma Notation
Evaluate.$$\sum_{k=0}^{2}(3 k+1)$$
Evaluate.$$\sum_{k=1}^{4}(3 k-1)$$
Evaluate.$$\sum_{k=0}^{3} 2^{k}$$
Evaluate.$$\sum_{k=1}^{4} \frac{1}{2^{k}}$$
Evaluate.$$\sum_{k=0}^{3}(-1)^{k} 2^{k}$$
Evaluate.$$\sum_{k=0}^{3}(-1)^{k} 2^{j \cdot 1}$$
Evaluate.$$\sum_{k=2}^{4} \frac{1}{3^{k-1}}$$
Evaluate.$$\sum_{k=1}^{5} \frac{(-1)^{2}}{k !}$$
Evaluate.$$\sum_{i=0}^{3}\left(\frac{1}{2}\right)^{2 k}$$
Evaluate.$$\sum_{k=0}^{3}(-1)^{k}\left(\frac{1}{2}\right)^{2 k}$$
Express in sigma notation.$$1+3+5+7 \cdots \cdots+21$$
Express in sigma notation.$$1-3+5-7+\dots-19$$
Express in sigma notation.$$1 \cdot 2+2 \cdot 3+3 \cdot 4+\dots-35 \cdot 36$$
Express in sigma notation.$$\text { The lower sum } m_{1} \Delta x_{1}+m_{2} \Delta x_{2}+\cdots+m_{n} \Delta x_{n}$$
Express in sigma notation.$$\text { The upper } \operatorname{sum} M_{1} \Delta x_{i}+M_{2} \Delta x_{2}+\cdots+M_{n} \Delta x_{n}$$
Express in sigma notation.$$\text { The Rjemann sum } f\left(x_{i}^{*}\right) \Delta x_{1}+f\left(x_{2}^{*}\right) \Delta x_{2}+\cdots+f\left(x_{n}^{*}\right) \Delta x_{n}$$
Write the given sums as $\sum_{k=3}^{10} a_{k}$ and as $\sum_{i=0}^{7} a_{i+3}$$$\frac{1}{2^{3}}+\frac{1}{2^{4}}-\cdots-\frac{1}{2^{10}}$$
Write the given sums as $\sum_{k=3}^{10} a_{k}$ and as $\sum_{i=0}^{7} a_{i+3}$$$\frac{3^{3}}{3 !}+\frac{4^{4}}{4 !}+\cdots+\frac{10^{10}}{10 !}$$
Write the given sums as $\sum_{k=3}^{10} a_{k}$ and as $\sum_{i=0}^{7} a_{i+3}$$$\frac{3}{4}-\frac{4}{5}+\dots-\frac{10}{11}$$
Write the given sums as $\sum_{k=3}^{10} a_{k}$ and as $\sum_{i=0}^{7} a_{i+3}$$$\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\dots+\frac{1}{17}$$
Transform the first expression into the second by a change of indices.$$\sum_{k=2}^{10} \frac{k}{k^{2}+1} ; \quad \sum_{n=-1}^{7} \frac{n+3}{n^{2}+6 n+10}$$
Transform the first expression into the second by a change of indices.$$\sum_{n=2}^{12} \frac{(-1)^{n}}{n-1} ; \quad \sum_{i=1}^{11} \frac{(-1)^{k+1}}{k}$$
Transform the first expression into the second by a change of indices.$$\sum_{k=4}^{25} \frac{1}{k^{2}-9} ; \quad \sum_{n=7}^{28} \frac{1}{n^{2}-6 n}$$
Transform the first expression into the second by a change of indices.$$\sum_{k=0}^{15} \frac{3^{2 k}}{k !} ; \quad 81 \sum_{x=-2}^{13} \frac{3^{2 n}}{(n+2) !}$$
Express the decimal fraction $0 . a_{1} a_{2} \cdots a_{n}$ in sigma notation using powers of $1 / 10$.
$$\text { Show that } \sum_{k=1}^{n} \frac{1}{\sqrt{k}} \geq \sqrt{n}$$
Use a graphing utility or CAS to evaluate the sum.$$\sum_{k=0}^{50} \frac{1}{4^{k}}$$
Use a graphing utility or CAS to evaluate the sum.$$\sum_{k=1}^{50} \frac{1}{k^{2}}$$
Use a graphing utility or CAS to evaluate the sum.$$\sum_{k=0}^{50} \frac{1}{k !}$$
Use a graphing utility or CAS to evaluate the sum.$$\sum_{k=0}^{50}\left(\frac{2}{3}\right)^{k}$$