series - induction - integration revision (2 Viewers)

[fullonoob]

Another thread to revise on the whole terms work
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]

damn no questions asked
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

 

[thongetsu]

lol why dont you just look at the questions in other threads?

 

[fullonoob]

show me induction inequality please ><
only did one question lol

 

[fullonoob]

lol why dont you just look at the questions in other threads?

alrdy did

 

[SeCKSiiMiNh]

use the terry lee book. there's some pretty crazy induction questions there.

 

[fullonoob]

use the terry lee book. there's some pretty crazy induction questions there.

i only have cambridge book right now

 

[fullonoob]

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]

Given that Tn = 2T(n-1) +1 and T1 = 5, prove that Tn = 6 x 2^(n-1) - 1

 

[SeCKSiiMiNh]

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

u sure you didnt write that question down wrong?

 

[fullonoob]

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

 

[ninetypercent]

maybe not, because 1/2 k^2 may not be an integer.

 

[SeCKSiiMiNh]

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]

Given that Tn = 2T(n-1) +1 and T1 = 5, prove that Tn = 6 x 2^(n-1) - 1

help me on this one please
this one i really need help on

 

[fullonoob]

maybe not, because 1/2 k^2 may not be an integer.

then how do you do it
exact same thing i was thinking
dno how to do the question posted too xD
i got both sides equal after i diffed it

 

[fullonoob]

i got both my ones now

 

[fullonoob]

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
you get dx / dx which cancels out when you product rule
never knew that a function can be cancelled out with a value :O

 

[SeCKSiiMiNh]

yay got this one
you get dx / dx which cancels out when you product rule
never knew that a function can be cancelled out with a value :O

how did you do it?!?! o.o

 

[fullonoob]

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