Question

How to simplify?

(n+1)!/n!

Answer 1

(n+1)! you can rewrite as (n+1)n!

Answer 2

So the answer is (n+1)?

Answer 3

yes

Answer 4

So for (n+2)!/(n+3)!, the answer is just (n+2)/(n+3)?

Answer 5

um no what is (n+3)! equal to ?

Answer 6

(n+3)n! ??

Answer 7

(n+3)!=(n+3)(n+2)(n+1)n.. and so on

Answer 8

so you can rewrite that as (n+3)!=(n+3)(n+2)!

Answer 9

Wait, so (n+2)! equals (n+2)(n+1) ?

Answer 10

that is (n+2)(n+1)(n+0)(n-1)... and can go on , depends on what you have for n , lets say if we let n=1 we would have (1+2)(1+1)(1+0)(1-1) and that is because we have reached 0

Answer 11

oh wait we dont include the 0 until we reach 1 my mistake sorry

Answer 12

The problem says that it starts at n=1, so then that means that the answer for the second one is (n+3), right?

Answer 13

ok so for the second one we have
\[\frac{ (n+2)! }{ (n+3)! }=\frac{ (n+2)! }{ (n+3)(n+2)! }=\frac{ 1 }{ (n+3) }\]

Answer 14

Ah, ok! I see!

Answer 15

Thanks!

Answer 16

no problem :)