Sully's Gameshow Extraordinaire!

[Victor Sullivan]

?100 Results:
1st: ManBungalow: 1000 points!
2nd: mviola: 400 points
3rd: Metsfanmax: 200 points
4th: Me
5th: TheSaxlad: -50 points
6th: The Bison King: -100 points
7th: Fircoal: -200 points
8th: Army of GOD: -500 points

?118: 10 points per active mafia player you can list (no repeats!).

[Campin_Killer]

Fircoal
Victor_Sullivan
Commander9
Campin_Killer
Skoffin
Justinassss
TheSaxLad
Streaker
HaggisMcMuttin
Sensfan
Edocsil
/
MeDeFe
theherkman
Ilaid
VIolet
TA1LSGUNNER
freezie
TheWeirdOne
ga7
FloresDeMal
aage
safariguy5
kernov
Mr. Squirrel
Thezz
Fuzzylogic
jeraado
Gabriel13
LSU Tiger Josh
Karelpetajie
JudahsLion
Drabod
Flow250
mass miracle
dazerazer
lildanbassman

[rdsrds2120]

Hmmmmmmmmmmm yeesssssssss you neeed an operationnnn.

Doctor Barber.

-rd

[naxus]

Fircoal
Victor_Sullivan
Commander9
Campin_Killer
Skoffin
Justinassss
TheSaxLad
Streaker
HaggisMcMuttin
Sensfan
Edocsil
/
MeDeFe
theherkman
Ilaid
VIolet
TA1LSGUNNER
freezie
TheWeirdOne
ga7
FloresDeMal
aage
safariguy5
kernov
Mr. Squirrel
Thezz
Fuzzylogic
jeraado
Gabriel13
LSU Tiger Josh
Karelpetajie
JudahsLion
Drabod
Flow250
mass miracle
dazerazer
lildanbassman

+me

[Victor Sullivan]

naxus gets 10, Campin gets 330, and rds gets 40...lashes.

?119: What is the definition of loquacious, in your own words? (I give points for creativity... )

[Campin_Killer]

Blabbing your ass off while annying the others to the point of suicide

[Victor Sullivan]

Blabbing your ass off while annying the others to the point of suicide

Very nice! Rather sad at the lack of entries... 200 points!

?120: Army of GOD can take this one This time he isnt banned (I think)

[Campin_Killer]

What does that mean?

[Victor Sullivan]

What does that mean?

He will be asking the question

[TA1LGUNN3R]

Blabbing your ass off while annying the others to the point of suicide

Very nice! Rather sad at the lack of entries... 200 points!

?120: Army of GOD can take this one This time he isnt banned (I think)

lol give it time.

-Tails

[notyou2]

A Clock!!!!

[karelpietertje]

I want to participate in this gameshow, and judging from the opening post, i should at any time be able to score at least 30 points by checking here.
Why can't I right now >: (

[ManBungalow]

inb4 Army of GOD never posts in this thread again.

[notyou2]

Is there something we should know Mr mod?

[Victor Sullivan]

Army of GOD is currently thinking of a question to stump you all. I set the deadline for tomorrow, so he will be posting soon. If not, the privileges will be passed to someone else.

[Army of GOD]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

[Haggis_McMutton]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

Wait. For x=1, n=3 => [(1+1)^3 <= 1+1*3] <=> [2^3 <= 4] ... ?

[notyou2]

pi??

[Army of GOD]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

Wait. For x=1, n=3 => [(1+1)^3 <= 1+1*3] <=> [2^3 <= 4] ... ?

whoops, that's supposed to be greater than or equal to, not less than.

[TheSaxlad]

Its a trick question...

Army of God that I know hasnt got that much maths skill.

shame on you for fooling us army...

[notyou2]

*ducks*

[Victor Sullivan]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

Wait. For x=1, n=3 => [(1+1)^3 <= 1+1*3] <=> [2^3 <= 4] ... ?

whoops, that's supposed to be greater than or equal to, not less than.

Also, Haggis' example only proves AoG's statement for the values he used for x and n.

[Campin_Killer]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

(1+1)^2 ≤ 1+(2)(1)
2^2 ≤ 1+2
4≤3
No

X=1
N=2

(1+10)^2 ≤ 1+(2)(10)
11^2 ≤ 1+20
22 ≤ 21
NO


N=2
X=10

(1+19)^5 ≤ 1+(5)(19)
20^5 ≤ 1+ 95
100 ≤ 96

(1+5)^2 ≤ 1+(2)(5)
6^2 ≤ 1+10
(1)12 ≤ 11(-1)
12 ≥ -11

What now AoG? Only took me 15 minutes to figure it out
X=5
N=2

[Army of GOD]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

(1+1)^2 ≤ 1+(2)(1)
2^2 ≤ 1+2
4≤3
No

X=1
N=2

(1+10)^2 ≤ 1+(2)(10)
11^2 ≤ 1+20
22 ≤ 21
NO


N=2
X=10

(1+19)^5 ≤ 1+(5)(19)
20^5 ≤ 1+ 95
100 ≤ 96

(1+5)^2 ≤ 1+(2)(5)
6^2 ≤ 1+10
(1)12 ≤ 11(-1)
12 ≥ -11

What now AoG? Only took me 15 minutes to figure it out
X=5
N=2

I amended it, the left term is greater than or equal to the right, not less than or equal to. Look at all the examples you posted; the left term is always greater than the right (or equal). You've shown it's true for select values of x or N. You have to prove it for x and n in general.

[Haggis_McMutton]

Question whatever: Prove that (1+x)^n ≤ 1+nx where x > -1 and n is any integer that is greater than 1.

Wait. For x=1, n=3 => [(1+1)^3 <= 1+1*3] <=> [2^3 <= 4] ... ?

whoops, that's supposed to be greater than or equal to, not less than.

Allrighty then.

Proof by induction on n that: [(1+x)^n >= 1+nx] for any x in (-1, inf), n in N*.

P(1) : 1+x >= 1+x (True)
P(n): (1+x)^n >= 1+nx
P(n+1): (1+x)^(n+1) >= 1+(n+1)x <=>
(1+x)^(n+1) >= 1+ nx + x
Notice that if (1+x)^(n+1) >= (1+x)^n + x, then by P(n) (1+x)^(n+1) >= 1+nx+x so If i prove (1+x)^(n+1) >= (1+x)^n + x i get the result
x is in (-1, inf) so 1+x > 0 so i divide by (1+x)^n =>
1+x >= 1 + x/(1+x)^n <=>
x >= x/(1+x)^n

Now we have 2 cases:
1. x is in [0, inf) => 1 >= 1/(1+x)^n <=>
(1+x)^n >= 1
(1+x) is in [1, inf) so that's true for all n in N*

2. x is in (-1,0) => 1 <= 1/(1+x)^n <=>
(1+x)^n <= 1
(1+x) is now in (0,1) so that's again true for all n in N*

so P(n) implies P(n+1) for all n in N*