Mathematical Induction Question (1 Viewer)

[LostAuzzie]

Could someone please help me out with this question
Im stuck with how to write the answer out without making any assumptions no matter how obvious

Question:
Prove by mathematical Induction, n^3 > 2n^2 + n for all n>2

Your help would be much appreciated

 

[rama_v]

Could someone please help me out with this question
Im stuck with how to write the answer out without making any assumptions no matter how obvious

Question:
Prove by mathematical Induction, n^3 > 2n^2 + n for all n>2

Your help would be much appreciated

I dunno if this is right but could you do this?
n=k+1
Need to prove (k+1)³ - 2(k+1)² -(k+1) >0

LHS = (k+1)((k+1)²-2(k+1) -1)
= (k+1)((k² + 2k +1) - 2k -2 -1)
= (k+1)((k² -2))
but k>2 so (k+1)>0..and k² -2 >0 when k>2 also (draw a parabola and this becomes clear)

.: LHS = (k+1)((k² -2)) >0

therefore true for n=k+1

 

[haboozin]

this is a classic question, they tend to not put inequalities in 3u for induction because there is only a few of them and they can almost be memorised.

i like the way rama v solved it, im gonna use this method next time.
i hate the way my teacher does it.

 

[Raginsheep]

this is a classic question, they tend to not put inequalities in 3u for induction because there is only a few of them and they can almost be memorised.

i like the way rama v solved it, im gonna use this method next time.
i hate the way my teacher does it.

Correct me if Im wrong but this is a math induction question and thus you need to make and use an assumption. Proving it the way above is, although mathematically correct, not maths induction.

 

[rama_v]

Correct me if Im wrong but this is a math induction question and thus you need to make and use an assumption. Proving it the way above is, although mathematically correct, not maths induction.

lol yeah, i just skipped to the n=k+1 step. Technically it shold start off with n=3, then assume true for n=k and then my step (prove true for n=k+1). Just add the first two steps and then its true by mathematical induction...

 

[rama_v]

Could someone please help me out with this question
Im stuck with how to write the answer out without making any assumptions no matter how obvious

Question:
Prove by mathematical Induction, n^3 > 2n^2 + n for all n>2

Your help would be much appreciated

Hey mate u want to do nano technology too
I want do do that as well, at UTS, I'll probably be seeing you there next year

 

[thunderdax]

lol yeah, i just skipped to the n=k+1 step. Technically it shold start off with n=3, then assume true for n=k and then my step (prove true for n=k+1). Just add the first two steps and then its true by mathematical induction...

Er, no its not. To prove by mathematical induction you have to use the assumption.

 

[mattchan]

The assume statement is:
k^3 - 2k^2 - k > 0


Expand (k+1)^3 - 2(k+1)^2 -(k+1) >0 to get:

= k^3 - 2k + k^2 - 2
= k^3 - 2k^2 - k + (3k^2 - k - 2) - Input the Assume Statement and Fix it up
= k^3 - 2k^2 - k + (k - 1)( 3k + 2)

Therefore for above line:
k^3 - 2k^2 - k > 0
(k - 1)( 3k + 2) > 0 for k > 1 and k <-2/3. Thus for k> 2, (k - 1)( 3k + 2) > 0

Therefore inequality is true for n = k + 1

 

[rama_v]

Er, no its not. To prove by mathematical induction you have to use the assumption.

oh right, yep, sorry i didnt fully understand ur first point. Anyway me mate chan solved it above

 

[LostAuzzie]

Hey mate u want to do nano technology too
I want do do that as well, at UTS, I'll probably be seeing you there next year

Most likely so, unless I have a sudden urge to travel for a year
An unlikely occurrence but a possibility nonetheless

Anyway thanks everyone for your help, much appreciated :uhhuh: