수열 전체 문제

Evaluate a Binomial Coefficient

In the following exercises, evaluate.

ⓐ $\left(\begin{array}{c}7 \\ 1\end{array}\right)$ ⓑ $\left(\begin{array}{c}5 \\ 5\end{array}\right)$ ⓒ $\left(\begin{array}{c}9 \\ 0\end{array}\right)$ ⓓ $\left(\begin{array}{c}9 \\ 5\end{array}\right)$

Evaluate a Binomial Coefficient

In the following exercises, evaluate.

ⓐ $\left(\begin{array}{c}1 \\ 1\end{array}\right)$ ⓑ $\left(\begin{array}{c}15 \\ 15\end{array}\right)$ ⓒ $\left(\begin{array}{c}4 \\ 0\end{array}\right)$ ⓓ $\left(\begin{array}{c}11 \\ 2\end{array}\right)$

Use the Binomial Theorem to Expand a Binomial

In the following exercises, expand each binomial, using the Binomial Theorem.

${(p+q)}^{6}$

Use the Binomial Theorem to Expand a Binomial

In the following exercises, expand each binomial, using the Binomial Theorem.

${(t-1)}^{9}$

Use the Binomial Theorem to Expand a Binomial

In the following exercises, expand each binomial, using the Binomial Theorem.

${(2x+1)}^{4}$

Use the Binomial Theorem to Expand a Binomial

In the following exercises, expand each binomial, using the Binomial Theorem.

${(4x+3y)}^{4}$

Use the Binomial Theorem to Expand a Binomial

In the following exercises, expand each binomial, using the Binomial Theorem.

${(x-3y)}^{5}$

In the following exercises, find the indicated term in the expansion of the binomial.

Seventh term of ${(a+b)}^{9}$

In the following exercises, find the indicated term in the expansion of the binomial.

Third term of ${(x-y)}^{7}$

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial.

${y}^{4}$ term of ${(y+3)}^{6}$

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial.

${x}^{5}$ term of ${(x-2)}^{8}$

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial.

${a}^{3}{b}^{4}$ term of ${(2a+b)}^{7}$

In the following exercises, write the first five terms of the sequence whose general term is given.

${a}_{n}=\frac{5n-3}{{3}^{n}}$

In the following exercises, write the first five terms of the sequence whose general term is given.

${a}_{n}=\frac{(n+2)!}{(n+3)!}$

In the following exercises, write the first five terms of the sequence whose general term is given.

Find a general term for the sequence, $-\frac{2}{3},-\frac{4}{5},-\frac{6}{7},-\frac{8}{9},-\frac{10}{11},\ldots$

Expand the partial sum and find its value. $\sum_{i=1}^{4}{(-4)}^{i}$

In the following exercises, write the first five terms of the sequence whose general term is given.

Write the following using summation notation. $-1+\frac{1}{4}-\frac{1}{9}+\frac{1}{16}-\frac{1}{25}$

Write the first five terms of the arithmetic sequence with the given first term and common difference. ${a}_{1}=-13$ and $d=3$

Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is $-7.$

Find the twenty-third term of an arithmetic sequence whose seventh term is $11$ and common difference is three. Then find a formula for the general term.