Consider n On 1 a Show that the equality is true bWhat are

Consider n! = O((n + 1)!).

(a) Show that the equality is true.

(b)What are all valid values of n0 when c = 1?

Solution

a.) Given f(n) = n!

Now, for f(n) = O(g(n))

c.g(n) >= f(n)

So, for c =2, and n0 >= 1

2.n! > n!

Hence, f(n) = O(n!)

Since, f(n) = O(n!). Therefore, it can be O((n+1)!), O((n+2)!) ..

Hence, n! = O((n+1)!).

2.) for c = 1, n0 >= 0.