Question

Decide whether each of the following is true or false:

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

Answer 1

True

Answer 2

is there any way this needs to be written out? so I can prove it by repeating the steps to reach the answer of (n + 1)! ?

Answer 3

Google it

Answer 4

n!(n + 1) = (n + 1)!
Factorial pretty much means multiplied by every number less than it until one (0! = 1 though).

So, 6! would be 6 * 5 * 4 * 3 * 2 * 1.
Notice how this is just 5! times 6.
5! = 5 * 4 * 3 * 2 * 1
5! * 6 = 6* (5 * 4 * 3 * 2 * 1)

If instead of 5 we had n and 6 we had n + 1, then this would still hold.
So, we could write:
(n+1)! = (n)! * (n+1)

The only difference between (n+1)! and n! is that the former has one extra term (by definition).