Chapter 13

After reading this secrion, write out the answers to these questions. Use complete sentences. What is Pascal's triangle and how do you make it?

Find the sum of each series. $$\sum_{i=1}^{5} i$$

Evaluate each expression. $$\frac{4 !}{4 ! 0 !}$$

List all terms of each finite sequence. \(a_{n}=2 n\) for \(1 \leq n \leq 5\)

Find the sum of each series. $$\sum_{i=1}^{6} 2 i$$

Evaluate each expression. $$\frac{5 !}{5 ! 0 !}$$

List all terms of each finite sequence. \(a_{n}=2 n-1\) for \(1 \leq n \leq 4\)

Find the sum of each series. $$\sum_{i=1}^{4} i^{2}$$

Evaluate each expression. $$\frac{5 !}{2 ! 3 !}$$

List all terms of each finite sequence. \(a_{n}=n^{2}\) for \(1 \leq n \leq 8\)

Find the sum of each series. $$\sum_{j=0}^{3}(j+1)^{2}$$

Evaluate each expression. $$\frac{6 !}{5 ! 1 !}$$

List all terms of each finite sequence. \(a_{n}=-n^{2}\) for \(1 \leq n \leq 4\)

Find the sum of each series. $$\sum_{j=0}^{5}(2 j-1)$$

Evaluate each expression. $$\frac{8 !}{5 ! 3 !}$$

List all terms of each finite sequence. \(b_{n}=\frac{(-1)^{n}}{n}\) for \(1 \leq n \leq 10\)

Find the sum of each series. $$\sum_{i=1}^{6}(2 i-3)$$

Evaluate each expression. $$\frac{9 !}{2 ! 7 !}$$

List all terms of each finite sequence. \(b_{n}=\frac{(-1)^{n+1}}{n}\) for \(1 \leq n \leq 6\)

Find the sum of each series. $$\sum_{i=1}^{5} 2^{-i}$$

Use the binomial theorem to expand each binomial. $$(x+1)^{3}$$

List all terms of each finite sequence. \(c_{n}=(-2)^{n-1}\) for \(1 \leq n \leq 5\)

Find the sum of each series. $$\sum_{i=1}^{5}(-2)^{-i}$$

Use the binomial theorem to expand each binomial. $$(y+1)^{4}$$

List all terms of each finite sequence. \(c_{n}=(-3)^{n-2}\) for \(1 \leq n \leq 5\)

Find the sum of each series. $$\sum_{i=1}^{10} 5 i^{0}$$

Use the binomial theorem to expand each binomial. $$(a+2)^{3}$$

List all terms of each finite sequence. \(a_{n}=2^{-n}\) for \(1 \leq n \leq 6\)

Find the sum of each series. $$\sum_{i=1}^{20} 3$$

Use the binomial theorem to expand each binomial. $$(b+3)^{3}$$

List all terms of each finite sequence. \(a_{n}=2^{-n+2}\) for \(1 \leq n \leq 5\)

Use the binomial theorem to expand each binomial. $$(r+t)^{5}$$

List all terms of each finite sequence. \(b_{n}=2 n-3\) for \(1 \leq n \leq 7\)

Find the sum of each series. $$\sum_{i=0}^{5} i(i-1)(i-2)(i-3)$$

Use the binomial theorem to expand each binomial. $$(r+t)^{6}$$

List all terms of each finite sequence. \(b_{n}=2 n+6\) for \(1 \leq n \leq 7\)

Use the binomial theorem to expand each binomial. $$(m-n)^{3}$$

List all terms of each finite sequence. \(c_{n}=n^{-1 / 2}\) for \(1 \leq n \leq 5\)

List all terms of each finite sequence. \(c_{n}=n^{1 / 2} 2^{-n}\) for \(1 \leq n \leq 4\)

Use the binomial theorem to expand each binomial. $$(x+2 a)^{3}$$

Write the first four terms of the infinite sequence whose nth term is given. \(a_{n}=\frac{1}{n^{2}+n}\)

Use the binomial theorem to expand each binomial. $$(a+3 b)^{4}$$

Write the first four terms of the infinite sequence whose nth term is given. \(b_{n}=\frac{1}{(n+1)(n+2)}\)

Use the binomial theorem to expand each binomial. $$\left(x^{2}-2\right)^{4}$$

Write the first four terms of the infinite sequence whose nth term is given. \(b_{n}=\frac{1}{2 n-5}\)

Write the first four terms of the infinite sequence whose nth term is given. \(a_{n}=\frac{4}{2 n+5}\)

Use the binomial theorem to expand each binomial. $$(x-1)^{7}$$

Write the first four terms of the infinite sequence whose nth term is given. \(c_{n}=(-1)^{n}(n-2)^{2}\)

Use the binomial theorem to expand each binomial. $$(x+1)^{6}$$

Write the first four terms of the infinite sequence whose nth term is given. \(c_{n}=(-1)^{n}(2 n-1)^{2}\)