Question

How do you expand n! and (n+1)!

For example, how would I simplify lim
`\lim_(n \to \infty) n!/(n+1)!`

Answer 1

Explanation:

n! = n × n−2 × n−3 × ... × 2 × 1

(n+1)! = n+1 × n × n−2 × n−3 × ... × 2 × 1

(n+1)! = (n+1) n!

Therefore:

lim(n→∞) (n! / (n+1)!)

lim(n→∞) (n! / ((n+1) n!))

lim(n→∞) (1 / (n+1))

0

Answer 2

n! = n × n−2 × n−3 × ... × 2 × 1

(n+1)! = n+1 × n × n−2 × n−3 × ... × 2 × 1

(n+1)! = (n+1) n!

Explanation: