Sequences: 동영상 및 연습문제

Use a calculator to evaluate the following expression:

48!/(48-2)!2!

Use a calculator to evaluate the following expression:

34!/(34-4)!

Use a calculator to evaluate the following expression. Approximate your answer, when necessary.

30!/225

Use a calculator to evaluate the following expression. Approximate your answer, when necessary.

(375/15)!

Use a calculator to evaluate the following expression:

158!/156!

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and any number of your choice, respectively. Do not evaluate.

(p + q) + (p + 3q) + (p + 5q) + ⋯ + [p + (2n - 1)q]

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as i and any number of your choice, respectively. Do not evaluate.

ar² + ar⁴ + ar⁶ + ar⁸ +...+ ar²⁴

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as i and any number of your choice, respectively. Do not evaluate.

4 + 9 + 14 + 19 +...+ 59

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and 1, respectively. Do not evaluate.

1 + 4 + 7 + ... + (3n - 2)

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and 1, respectively. Do not evaluate.

7 + 7²/2 + 7³/3 + ... + 7ⁿ/n

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and 1, respectively. Do not evaluate.

1/4 + 2/5 + 3/6 + ... + 20/(20 + 3)

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and 5, respectively. Do not evaluate.

5 + 6 + 7 + ... + 35

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and 1, respectively. Do not evaluate.

6 + 6² + 6³ + ... + 6²⁰

Rewrite the following sum using summation notation. Represent the index and lower limit of the summation as k and 1, respectively. Do not evaluate.

1⁶ + 2⁶ + 3⁶ + ... + 20⁶

Evaluate the indicated summation.

Evaluate the indicated summation.

Evaluate the indicated summation.

Evaluate the indicated summation.

Evaluate the indicated summation.

Evaluate the indicated summation.

Evaluate the indicated summation.

Consider the given factorial expression and completely simplify it.

(n+4)!/(n+5)!

Consider the given factorial expression and evaluate it. 

21!/2!19!

Consider the given factorial expression and evaluate it. 

23!/21! 

A factorial is used in the general term of a sequence, which is given. Write the sequence's first four terms. 

a_n = 3(2n-1)!

A factorial is used in the general term of a sequence, which is given. Write the sequence's first four terms. 

a_n = (n +1)²/(n +2)!

Write the first four terms of the sequence using the recursion formula. 

a₁ = 8 and a_n = 6a_n-1 + 1 for n≥2

Write the first four terms of the sequence using the recursion formula. 

a₁= 5 and a_n=7a_n-1 for n≥2

Write the first four terms of the sequence using the recursion formula. 

a₁=9 and a_n=a_n-1 + 2 for n≥2 

In the sequence whose general term is provided, write the first four terms. 

a_n = (−1)ⁿ⁺¹/(3ⁿ−1)