series - induction - integration revision (1 Viewer)

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
Another thread to revise on the whole terms work :drink:
Simply post questions on any of the above-mentioned topics and hope for them to be answered x)
Hmm the rule is whoever answers a question must ask a question in return, just like a marathon.
i'll start off with an easy one
Prove by induction that x^n - 1 is divisible by x-1 for n a positive integer and x>0
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
damn no questions asked :cry:
if anyone has difficult questions please post them up, tmr is my exam and i would like to kill it
Rep up for grabs if is hard :p
 

thongetsu

Where aren't I?
Joined
Nov 9, 2008
Messages
1,883
Gender
Male
HSC
2010
lol why dont you just look at the questions in other threads?
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
show me induction inequality please ><
only did one question lol
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
i got one i need help on answer fast please :)
you can skip all the steps and just go to prove n = k+1 or 2?
For even n prove n^3 + 2n is divisible by 12
advancing of the proof from k to k+2
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
Given that Tn = 2T(n-1) +1 and T1 = 5, prove that Tn = 6 x 2^(n-1) - 1
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
im sure i wrote it write
use k +2 instead
at the end i get 12m +6k^2 + 12k + 12
but im not sure if you're allowed to make the 6k^2 into 1/2 k^2
so i have 12 on the outside
 

SeCKSiiMiNh

i'm a fireball in bed
Joined
Mar 6, 2008
Messages
2,618
Location
island of screaming orgasms
Gender
Male
HSC
2009
im sure i wrote it write
use k +2 instead
at the end i get 12m +6k^2 + 12k + 12
but im not sure if you're allowed to make the 6k^2 into 1/2 k^2
so i have 12 on the outside
i got up to there as well.
i remember doing this question in mr lee's book though and i could've taken the 12 out perfectly.
=/

try this one:

prove by mathematical induction that

d/dx x^n = nx^n-1

this was in the hsc last year
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
i got up to there as well.
i remember doing this question in mr lee's book though and i could've taken the 12 out perfectly.
=/

try this one:

prove by mathematical induction that

d/dx x^n = nx^n-1

this was in the hsc last year
yay got this one :D
you get dx / dx which cancels out when you product rule
never knew that a function can be cancelled out with a value :O
 

fullonoob

fail engrish? unpossible!
Joined
Jul 19, 2008
Messages
465
Gender
Male
HSC
2010
for your one you dont diff it till the very end
after you assume n = k
you get some integral with x x^k d/dx
then you do product rule
you will get dx /dx on one side which then cancels out
then you only have d / dx on one side
diff that side
and you will prove n = k +1
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top