14. Sequences & Series

Evaluate the expression.

$\frac{12}{4!}$

Evaluate the expression.

$\frac{9!}{7!}$

Evaluate the expression.

$\frac{16!}{12!\cdot4!}$

Write the first 4 terms of the sequence $a_{n}=n^2\cdot\left(n-1\right)!$

Evaluate 1000!/998! without a calculator.

Simplify k! / (k + 2)! for any integer k ≥ 0.

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

b. (2n)! / (2n − 1)! = 2n

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. n!n! = (2n)! for all positive integers n.