Question

does anyone know how 2n+2! becomes (2n+2)(2n+1)

Answer 1

i guess it must b (2n +2)! ?

Answer 2

yah

Answer 3

n! = n(n-1)!

Answer 4

(2n+2)(2n+1) (2n)....1

Answer 5

(2n+2)!= (2n+2)(2n+1)!

Answer 6

on cramster one of the problem shows it changes from (2n+2)! and becomes (2n+1)(2n+2) with no factorial sign behind it

Answer 7

there is a facatorial behind it......

Answer 8

i mean they don't show it like this (2n+2)(2n+1) (2n)....1

Answer 9

I meant that u keep decreasing by 1 until u reach 1
another way of writing it (2n+2)(2n+1) (2n)...3.2.1

Answer 10

yah they dont show it decreasing it stops after 2n+1

Answer 11

yes but there must be a factorial with it

Answer 12

and there isnt

Answer 13

As far as I know about factorials ...there should be...I could be wrong

Answer 14

is there anyway you can look at the problem on cramster

Answer 15

u can check on wolframalpha.com

Answer 16

there must be factorial with it

Answer 17

there has to be a factorial behind it, unless there is something else about your problem... cramster sometimes has mistakes

Answer 18

the things is my teacher did the same thing so im confused

Answer 19

the only way the factorial can drop out is if it cancelled out in a fraction

Answer 20

then check did u post the right question?

Answer 21

this is the actual problem determine of this series converges or diverges\[\sum_{n=1}^{\infty} (n!)^2/(2n) !\]

Answer 22

use ratio test

Answer 23

n u applied some test for the convergence of series?

Answer 24

right

Answer 25

i did but i didnt correct answer if someone can please show me how to do this it can help me with the rest of my problems

Answer 26

sigh i hate it when people post half the question... thigns cancel and become (n+1)^2/(2n+2)(2n+1)

Answer 27

what is 2n!

Answer 28

yes it converges, so you use ratio test...

an+1/an= [ ((n+1)!)^2/(2(n+1))! ]/ [ (n!)^2/(2n)! ]

flipping fractions to get 1 whole one..

(2n)!(n+1)!(n+1)!/(n!)(n!)(2n+2)!
which is where your question arises, like I said, the only reason the factorial disappeared is cause it got cancelled, which you always want to do when doing ratio test, so you simply keep pulling your factorials apart until they can cancel

so on top (n+1)!=(n+1)(n!), which you do twice to get rid of both the n! on the bottom

then on the bottom you have (2n+2)! so you pull the factorial apart twice to get (2n+2)(2n+1)(2n)! then the (2n)! can cancel with the one on top and you get left with (n+1)^2/(2n+2)(2n+1). take the limit and it should be 1/4 so it converges

Answer 29

yes i was able to catch my mistake thank you very much. i wanted to know how does 2n! decrease

Answer 30

does it become (2n)(2n-1)(2n-2)..1

Answer 31

yes

Answer 32

hey thank u for ur help im gonna become a fan