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C)R
Canada549 Posts
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. | ||
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ProudToBeANoob
Thailand54 Posts
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LpThaPro
Canada21 Posts
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 | ||
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ProudToBeANoob
Thailand54 Posts
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... | ||
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Commander{+}
United States2878 Posts
On September 23 2003 04:17 BigBalls wrote: 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! | ||
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C)R
Canada549 Posts
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
France1270 Posts
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 | ||
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X)Benny
France1270 Posts
 let me think more... | ||
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ProudToBeANoob
Thailand54 Posts
On September 23 2003 07:47 C)R wrote: 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). | ||
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X)Benny
France1270 Posts
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  | ||
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ProudToBeANoob
Thailand54 Posts
Sorry for non-speaking french, i just ask :p hard to come back to 8 years ago... | ||
Liquid`Drone
Norway28665 Posts
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. | ||
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X)Benny
France1270 Posts
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BinGBonG[gamei]
Netherlands514 Posts
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BigBalls
United States5354 Posts
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 | ||
Mynock
4492 Posts
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 | ||
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KiDDy
Finland12 Posts
 my opinion about USA  and  so damn selfcentered country. i'm pretty neutral about the french. | ||
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iD.GioM
France99 Posts
Blackjack is retarded man I told u I've experienced it ? And u havent been in war with france have u ? so stfu ? thx ! | ||
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ayer
Mexico164 Posts
It doesn't matter the whole point of this thread for us to realize we are all human and have buttsex with each other! | ||
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BlackJack
United States10495 Posts
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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