Question

Can someone explain how..

typing problem.

Answer 1

\[\frac{ (n+1)^{n+1} }{ (n+1)! } * \frac{ n! }{ n ^{n} } = \frac{ (n+1) }{ n ^{n} }\]

Answer 2

I forgot factorials.

Answer 3

I know its a simple concept. I just need an explanation please.

Answer 4

woops. it is = (n+1)^n / n^n

Answer 5

The simplified expression should be \[\left(\frac{n+1}{n}\right)^n\]

Answer 6

yes

Answer 7

Just notice that \((n+1)!=n!(n+1)\)

Answer 8

I still cannot grasp it.. lol idk why.

Answer 9

5! = 5 * 4 * 3 * 2 * 1
so n! = n!(n-1)

Answer 10

can you cancel anything?

Answer 11

You cancel the n!(n+1) right?

Answer 12

yes, so what do you have after canceling that?

Answer 13

(n+1)^n+1 / n^n

Answer 14

be careful! you cancel one of the n+1 so you have \((n+1)^n\) now

Answer 15

im sorry.. im trying to understand. lol

so n! = n!(n-1) yes?

Answer 16

no, that is incorrect! In the simplification we don't change the \(n!\) we just rewrite \((n+1)!=n!(n+1)\)

Answer 17

OHHHHHHHHHHH

Answer 18

so then (n+1)^n and (n+1) reduces to (n+1)^n

Answer 19

the n1's cancel out.