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Why I hate the french - Page 10

Forum Index > General Forum
Post a Reply
Prev 1 8 9 10 11 Next All
C)R
Profile Joined October 2002
Canada549 Posts
September 22 2003 20:21 GMT
#181
kk, u made me open the damn book, I'm not going to put the effort in to solve all the steps but I'll give you what my old book has. It basically has the same question but gives you clues to solving.

an = (1 + 1/n)^n
First (a) it wants you to show that if 0<=a<b
[b^(n+1)-a^(n+1)]/b-a < (n+1)b^n
then, (b)
deduce that b^n[(n+1)a-nb] < a^(n+1)
then, (c)
use a = 1+1/(n+1)
b = 1+1/n
in part (b) to show that {an} is increasing

I hope this helps. Basically what you want is part c but it looks like you need to do part a,b for it to make sense.

ProudToBeANoob
Profile Joined July 2003
Thailand54 Posts
September 22 2003 20:56 GMT
#182
just a remark like that, but is it not useful to take the exp formula of (1+1/x)^x, and using the fact that both log and exp are increasing functions ? I don't remember well all the conditions to say that f(something increasing) with f increasing is also increasing (i think that everything should be strictly positive which is the case), maybe i am totally wrong...
It sounds like...a huge, gargantuan, swollen, bloated mushroom!
LpThaPro
Profile Joined September 2003
Canada21 Posts
Last Edited: 2003-09-23 17:17:51
September 22 2003 22:06 GMT
#183
Hey Smart Kid 'BigBalls', Since you are a Math major, I think you should be more respectful and thankful to France as it is THE country which contributed the most in the history of mathematics.

Oh yeah, by the way, France is THE most visited country in the World and by far.
I think you should go there and realize that there are far more important things in life than military victories.

-Peace
I shall remain faithful to God......
ProudToBeANoob
Profile Joined July 2003
Thailand54 Posts
September 22 2003 22:13 GMT
#184
I totally agree, but please, don't send more people in France to visit, they will discover how badly we welcome tourists :p

Anyway, fed up with this 'gueguerres' usa/france and antiUSA/proUSA, it doesn't lead anywhere and just enforces stupidity where it already stands strong...
It sounds like...a huge, gargantuan, swollen, bloated mushroom!
Commander{+}
Profile Joined December 2002
United States2878 Posts
September 22 2003 22:17 GMT
#185
On September 23 2003 04:17 BigBalls wrote:
Show nested quote +
On September 23 2003 02:32 C)R wrote:
big balls you have to show that
lets say you're sequence is An (imagine the n is subscript)
you need to prove that An+1 > An
so... do cross multiplication and simplify to show something obvious
i don't think u even need to simplify because you can just say
n + 1 will always be a higher power or just describe why its >

I think i was taught the fancy way to argue that but it escapes me now

heh now that i think about it (1+1/n)^n is the number e so yeah your question is ez.



i know its e, but i have to prove it is strictly increasing, thats the point of the exercise .

i did cross multiply. i got (n+1)^2n+1 <= n^n * (n+2)^n+1 its not intuitively obvious that one is larger than the other. I tried induction and it wasnt working out (assume this is true and then show that (n+2)^2n+3 <= n+1^n+1 * (n+3)^n+2 I couldnt get it to show this last step.


Tutor me... bitch!
4 cheers for Ryan307
C)R
Profile Joined October 2002
Canada549 Posts
September 22 2003 22:47 GMT
#186
On September 23 2003 05:56 ProudToBeANoob wrote:
just a remark like that, but is it not useful to take the exp formula of (1+1/x)^x, and using the fact that both log and exp are increasing functions ? I don't remember well all the conditions to say that f(something increasing) with f increasing is also increasing (i think that everything should be strictly positive which is the case), maybe i am totally wrong...


this isn't a function, it's an infinite series, you can only prove it's increasing (by definition) by showing an<=an+1 for all n>=1
X)Benny
Profile Joined October 2002
France1270 Posts
September 23 2003 01:58 GMT
#187
LeJester,
you've got a point. So I'll put it this way.
Saying that "any food in the world is better than US food" is just my opinion, you don't have to take it. Well at least this opinion is based on experience: I've spent 5 months in the US, 6 in Canada, 1 in Bolivia, 1 in Japan... As for Blackjack and snails, I guess he never tried them, I guess he has never been to France either, so how can he claim bigmac>snails?

BigBalls,
Sorry I left work just when you released your problem. I'm glad we got back to more serious talks.
An=(n+1/n)^n
An+1=(n+2/n+1)^(n+1)
An+1/An=(n+2/n+1)*(n+2/n)^n > 1

gg
X)Benny
Profile Joined October 2002
France1270 Posts
September 23 2003 02:02 GMT
#188
oups.... sorry, there's a mistake in the calculation, mornings don't help me think.
let me think more...
ProudToBeANoob
Profile Joined July 2003
Thailand54 Posts
Last Edited: 2003-09-23 02:18:16
September 23 2003 02:16 GMT
#189
On September 23 2003 07:47 C)R wrote:
Show nested quote +
On September 23 2003 05:56 ProudToBeANoob wrote:
just a remark like that, but is it not useful to take the exp formula of (1+1/x)^x, and using the fact that both log and exp are increasing functions ? I don't remember well all the conditions to say that f(something increasing) with f increasing is also increasing (i think that everything should be strictly positive which is the case), maybe i am totally wrong...


this isn't a function, it's an infinite series, you can only prove it's increasing (by definition) by showing an<=an+1 for all n>=1


So what? If it works for every x in IR+*, it works for every n in IN*.
Proving f(a)<f(b) if a<b => an=f(n)<an+1=f(n+1) for n>=1.
But what i doubt about my remark is just the condition to say that fog(x) is increasing when g is increasing, it's a long time ago, i forgot it...

Anyway Benny's try seems a good way...Or we can try 'par recurrence' (i don't know the word in english).
It sounds like...a huge, gargantuan, swollen, bloated mushroom!
X)Benny
Profile Joined October 2002
France1270 Posts
September 23 2003 02:39 GMT
#190
oki;
it's not very smart but it works:
let f(x)=(1+1/x)^x , we want to show f increases in R+
f'(x)=[ln(1+1/x) - 1/1+x]*exp(...), we want to show f'>0
g(x)=f'/exp(...), we want to show g>0
g'(x)=1/(1+x)^2 - 1/x*(1+x) < 0
so g decreases. Since we also have lim(x->+oo) g = 0, it means g>0.

gg
ProudToBeANoob
Profile Joined July 2003
Thailand54 Posts
Last Edited: 2003-09-23 03:04:50
September 23 2003 03:01 GMT
#191
hola je pensais pas qu'il fallait deriver etc...Y a pas juste un theoreme qui dit si g croissante et strictement positive (ici xlog(1+1/x) qui l'est si x>0), et si f est croissante (exp l'est par definition), alors fog (la composee de g par f) est croissante ? Peut-etre qu'il faut plus que la stricte positivite (de plus, je vois meme pas pourquoi l'imposer, donc chuis ptet a la rue)...

Sorry for non-speaking french, i just ask :p

hard to come back to 8 years ago...
It sounds like...a huge, gargantuan, swollen, bloated mushroom!
Liquid`Drone
Profile Joined September 2002
Norway28664 Posts
September 23 2003 03:49 GMT
#192
:E

shasta, if someone made a funny joke about norway, I'd laugh at it.
if someone made a funny joke about my mother, I'd laugh. if someone makes a funny joke about me, I laugh.

to everyone from north america who has said "the world hates the french because" or anything similar to that, you forget something. the world doesn't hate the french. europeans don't hate the french. the world hates USA. and for plenty of more better reasons than anyone has for hating the french!

but hating based on nationality is pretty fucking retarded in the first place. : )

likewise, everyone who are "proud" to be of any nationality are a bunch of fucking morons.
Moderator
X)Benny
Profile Joined October 2002
France1270 Posts
September 23 2003 04:28 GMT
#193
This old post is unavailable due to an encoding issue. Please contact an admin if you would like this post restored for historical reasons.
BinGBonG[gamei]
Profile Joined May 2003
Netherlands514 Posts
September 23 2003 05:55 GMT
#194
HOLLAND !!! HOLLAND!! HOLLAND!!! hehe idiots =P
Smoke weed everyday ~-_-~
BigBalls
Profile Blog Joined May 2003
United States5354 Posts
September 23 2003 08:43 GMT
#195
On September 23 2003 11:39 X)Benny wrote:
oki;
it's not very smart but it works:
let f(x)=(1+1/x)^x , we want to show f increases in R+
f'(x)=[ln(1+1/x) - 1/1+x]*exp(...), we want to show f'>0
g(x)=f'/exp(...), we want to show g>0
g'(x)=1/(1+x)^2 - 1/x*(1+x) < 0
so g decreases. Since we also have lim(x->+oo) g = 0, it means g>0.

gg


cant use that. i used ln in one of my epsilon proofs and he said we werent allowed to use it yet.


i think im onto something. it has to do with the binomial expansion of n and n+1.

the n+1 expansion has a term that dominates everything in the n expansion. i think this is the best way to go about it.

gg :o
if you guys could use google and post direct links to the maphacks here it would be greatly appreciated. - Nazgul
Mynock
Profile Joined September 2002
4492 Posts
September 23 2003 09:52 GMT
#196
On September 23 2003 12:49 Liquid`Drone wrote:
:E

shasta, if someone made a funny joke about norway, I'd laugh at it.
if someone made a funny joke about my mother, I'd laugh. if someone makes a funny joke about me, I laugh.

to everyone from north america who has said "the world hates the french because" or anything similar to that, you forget something. the world doesn't hate the french. europeans don't hate the french. the world hates USA. and for plenty of more better reasons than anyone has for hating the french!

but hating based on nationality is pretty fucking retarded in the first place. : )

likewise, everyone who are "proud" to be of any nationality are a bunch of fucking morons.


Humm Drone... pretty nice.

-Mynock
KiDDy
Profile Joined August 2003
Finland12 Posts
Last Edited: 2003-09-23 10:06:05
September 23 2003 10:01 GMT
#197
drone seems like a wise guy... nice.

my opinion about USA and
so damn selfcentered country.

i'm pretty neutral about the french.
hoilaa..
iD.GioM
Profile Joined June 2003
France99 Posts
September 23 2003 10:43 GMT
#198
Drone is sooooo sexy !
Blackjack is retarded
man I told u I've experienced it ?
And u havent been in war with france have u ? so stfu ? thx !
ayer
Profile Joined February 2003
Mexico164 Posts
September 23 2003 11:07 GMT
#199
On September 22 2003 23:22 BigBalls wrote:
Show nested quote +
On September 22 2003 23:03 ayer wrote:
appears with a shotgun held tightly with both hands*a deafening clap*BigBalls futile crys fly into the air


you albanian?

It doesn't matter the whole point of this thread for us to realize we are all human and have buttsex with each other!
BlackJack
Profile Blog Joined June 2003
United States10490 Posts
September 23 2003 11:52 GMT
#200
On September 23 2003 19:43 iD.GioM wrote:
Drone is sooooo sexy !
Blackjack is retarded
man I told u I've experienced it ?
And u havent been in war with france have u ? so stfu ? thx !


I have no idea what you are talking about
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