Question

Please, explain me

Answer 1

I don't understand last line

Answer 2

me neither, it should be \(\large \left|\dfrac{4}{n+2}\right|\)

Answer 3

Thank you!! I feel like dummy when I can't understand how they get it !! ( from the book)

Answer 4

mostly a typo I hope :)

Answer 5

@ganeshie8 help me with this problem, please.
Prove that the order of a permutation in \(S_n\) divides n!
How to start?

Answer 6

Iis it not that order of permutation in S_n is n and n! = n*(n-1) *..... which shows it divides n!

Answer 7

But I don't think that problem is so simple like that

Answer 8

Woah! I don't understand the question... whats S_n ?

Answer 9

May be it is a set of n elements

Answer 10

Oh, It is set of Symmetry of set of n elements
Ha!! I am so bad at explanation.
X = {x1,x2,....,xn}
Symmetry ({X}) denoted by \(S_n\)

Answer 11

http://en.wikipedia.org/wiki/Symmetric_group

Answer 12

Not sure I may not be useful here as idk abstract algebra

Answer 13

It says a much stronger statement : order of symmetric group of n elements itself is n!

Answer 14

That's good enough, thank you.
One more thing: On the paper I attached, the right hand side of the fist line should be \(|\dfrac{-4}{n+2}|\) right?

Answer 15

signs shouldnt matter as absolute bars fixes them :

|-4| = |4|

Answer 16

Ok, it is clear now. :)

Answer 17

If n> N
can we assume that \(\dfrac {\sqrt n}{n+1}< \dfrac{\sqrt N}{N+1}\)

Answer 18

yes

\(\large \dfrac{1}{n+1} \lt \dfrac{1}{n}\)

Answer 19

plugin n = 1

Answer 20

\(\large \dfrac{1}{1+1} \lt \dfrac{1}{1}\)

Answer 21

You mean I have to use induction to prove it before using the result to continue my stuff??

Answer 22

nope, its just a mind game... proof is not needed i think

Answer 23

1/2 < 1

what proof do u want for this ?

Answer 24

hmm

Answer 25

1/(n+1) < 1/n

ofcourse presumably "n" is positive

Answer 26

I have to prove lim of a sequence =0, part of them is the expression above.
Since it is a proving problem, every single line must be proved.

Answer 27

that is a lot of proving
at some point something should be obvious without proof

Answer 28

@satellite73 but at least we have to have a logic to make a conclusion, right?

Answer 29

i feel it should be okay to use it without a proof, in limits proofs we use this all the time :

\[\large \dfrac{1}{n-1} \lt \epsilon \implies \dfrac{1}{n}\lt \epsilon \]

we can make conclusions like this in the back of head in proofs

Answer 30

its same as reasoning :

\[\large 10 \lt a \implies 9 \lt a\]

Answer 31

Got you, thanks for the help,:)

Answer 32

np :D