154k views
5 votes
How do you expand n! and (n+1)!

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

2 Answers

3 votes

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

User Bas Kuis
by
8.0k points
2 votes

Answer:

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:

User Georgy Kopshteyn
by
8.7k points

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