Math Induction (1 Viewer)

[Tryingtodowell]

Can I conclude that a negative answer is >= 0. I know that obviously you cannot for > only but since there is 'EQUAL TO' can I assume that?

 

[liamkk112]

Can I conclude that a negative answer is >= 0. I know that obviously you cannot for > only but since there is 'EQUAL TO' can I assume that?

negative number, by defintion, is < 0. similarly, positive number is > 0, non-negative is >= 0, non-positive is <= 0 . so i dont think u can conclude that a negative answer is >= 0, i think u might mean that can i say that a non-positive number is >= 0, similarly no, unless if the number is exactly zero.

 

[Tryingtodowell]

negative number, by defintion, is < 0. similarly, positive number is > 0, non-negative is >= 0, non-positive is <= 0 . so i dont think u can conclude that a negative answer is >= 0, i think u might mean that can i say that a non-positive number is >= 0, similarly no, unless if the number is exactly zero.

Can I conclude that -4k >=0 - for example

 

[Tryingtodowell]

Im struggling with this question:

Prove by MI that 2^2^n >= 5^2n for all integers n>=5

I did:

For n=5,

LHS=42967296
RHS=9765626

Therefore LHS>=RHS
Thus true

Assume true for n=k,

2^2^k >= 5^2k

RTP; n=k+1

2^2^k+1 >= 5^2k+2

LHS= 2^2^k . 2^2

>= 4(5^2k) - from assumption

RHS- LHS= 4(5^2k) - 25(5^2k)

>= -21(5^2k) = RHS

Therefore by P of MI.....

I feel like this is completely wrong and I dont know how to approach it

 

[liamkk112]

Can I conclude that -4k >=0 - for example

only if k <= 0. obviously if k >0, then any number u plug in for k will mean that -4k will be negative, so the result will be < 0

 

[Tryingtodowell]

only if k <= 0. obviously if k >0, then any number u plug in for k will mean that -4k will be negative, so the result will be < 0

Everytime I do that question above I end up getting a negative answer for a >= 0. I think im doing the question completely wrong

 

[liamkk112]

Im struggling with this question:

Prove by MI that 2^2^n >= 5^2n for all integers n>=5

I did:

For n=5,

LHS=42967296
RHS=9765626

Therefore LHS>=RHS
Thus true

Assume true for n=k,

2^2^k >= 5^2k

RTP; n=k+1

2^2^k+1 >= 5^2k+2

LHS= 2^2^k . 2^2

>= 4(5^2k) - from assumption

RHS- LHS= 4(5^2k) - 25(5^2k)

>= -21(5^2k) = RHS

Therefore by P of MI.....

I feel like this is completely wrong and I dont know how to approach it

starting from LHS = : for proving the result is true for n = k + 1:

we get that LHS =
then we can apply the assumption:
=> LHS

hence LHS >= RHS as required and hence by mathematical induction...

 

[liamkk112]

Everytime I do that question above I end up getting a negative answer for a >= 0. I think im doing the question completely wrong

yes, the inequality that -4k >= 0 only holds true for negative numbers, so if a >= 0 the inequality is false

 

[Tryingtodowell]

starting from LHS = : for proving the result is true for n = k + 1:

we get that LHS =
then we can apply the assumption:
=> LHS

hence LHS >= RHS as required and hence by mathematical induction...

THANK U SO MUCHH and btw how would you prove by MI that the sum of exterior angles of an n sided convex polygon is 360 like what do I say for n=k and n=k+1

 

[liamkk112]

THANK U SO MUCHH and btw how would you prove by MI that the sum of exterior angles of an n sided convex polygon is 360 like what do I say for n=k and n=k+1

u should draw the k sided polygon (you can draw one of any size greater or equal to the base case) which we assume to have a sum of exterior angles of 360 degrees, then draw the (k+1)th side onto this k sided polygon to make the k+1 polygon, then think about what changes when you added the (k+1)th side

 

[Tryingtodowell]

u should draw the k sided polygon (you can draw one of any size greater or equal to the base case) which we assume to have a sum of exterior angles of 360 degrees, then draw the (k+1)th side onto this k sided polygon to make the k+1 polygon, then think about what changes when you added the (k+1)th side

ughh I hate this imao how important is this topic in 3u and 4u? Like does it appear much in exams etc

 

[liamkk112]

ughh I hate this imao how important is this topic in 3u and 4u? Like does it appear much in exams etc

geometric induction is annoying af lol. usually you wouldnt get a question like this as it is basically a textbook example of a geometric induction question, you would more get different applications, check out question 12d of this paper:

https://educationstandards.nsw.edu.au/wps/wcm/connect/385e2f4e-b868-4c1e-97f4-56befe81375d/mathematics-ext-2-sample-examination-materials-2020.pdf?MOD=AJPERES&CVID=

 

[Tryingtodowell]

geometric induction is annoying af lol. usually you wouldnt get a question like this as it is basically a textbook example of a geometric induction question, you would more get different applications, check out question 12d of this paper:

Talking about mathematical induction in general does it appear much? Fingers crossed it doesnt

 

[liamkk112]

Talking about mathematical induction in general does it appear much? Fingers crossed it doesnt

yea theres always at least 1 3u question, and usually 1 in 4u too. though, they are usually in the earlier questions (11-14) from memory so they are not too difficult, and most of them are quite straightforward once u get the hang of it

 

[WeiWeiMan]

geometric induction is annoying af lol. usually you wouldnt get a question like this as it is basically a textbook example of a geometric induction question, you would more get different applications, check out question 12d of this paper:

https://educationstandards.nsw.edu.au/wps/wcm/connect/385e2f4e-b868-4c1e-97f4-56befe81375d/mathematics-ext-2-sample-examination-materials-2020.pdf?MOD=AJPERES&CVID=

12d is a very nice question i must say

Talking about mathematical induction in general does it appear much? Fingers crossed it doesnt

in 3u it's not rly applying to anything so you're rly just proving some series sum or divisibility
for 3u induction is free marks
idk about 4u i haven't done that yet

 

[liamkk112]

12d is a very nice question i must say


in 3u it's not rly applying to anything so you're rly just proving some series sum or divisibility
for 3u induction is free marks
idk about 4u i haven't done that yet

yea true about 3u induction coz its only sums and divisibility, however they can get u with some sneaky sums where u can miss a term if you dont think carefully but in general it is free marks. just be really good at structuring ur answer, my teacher is a hsc marker and she said if u dont write out everything very clearly, u can easily lose 1 mark just for the structure

 

[Tryingtodowell]

12d is a very nice question i must say


in 3u it's not rly applying to anything so you're rly just proving some series sum or divisibility
for 3u induction is free marks
idk about 4u i haven't done that yet

yeah those are ez

 

[Tryingtodowell]

yea true about 3u induction coz its only sums and divisibility, however they can get u with some sneaky sums where u can miss a term if you dont think carefully but in general it is free marks. just be really good at structuring ur answer, my teacher is a hsc marker and she said if u dont write out everything very clearly, u can easily lose 1 mark just for the structure

inequality and geometric induction is such a bother for me ughh is that part of 3u? heard its in yr 12 and Im only starting yr 11 this year so idk

 

[liamkk112]

inequality and geometric induction is such a bother for me ughh is that part of 3u? heard its in yr 12 and Im only starting yr 11 this year so idk

no its only 4u content