help me (1 Viewer)

[coca cola]

this Q is from jeff geha's 50 tips, tip no.48 first example in induction.

this part i don't get:

1 + 1/4 + 1/9... 1/k^2 + 1/(k+1)^2 < 2 - 1/k + 1/(k+1)^2

. = 2 - (1/k - 1/[k(k+1)])

what i don't get is why does:

2 - 1/k + 1/(k+1)^2 = 2 - (1/k - 1/[k(k+1)])

doesn't 2 - 1/k + 1/(k+1)^2 < 2 - (1/k - 1/[k(k+1)]) instead?

what am i missing?

 

[steverulz55]

well usually by convention you read from top line to bottom line:

ie. for your case, 2 - 1/k + 1/(k+1)^2 = 2 - (1/k - 1/[k(k+1)]) as they are equal not one greater than other

NOT 1 + 1/4 + 1/9... 1/k^2 + 1/(k+1)^2 = 2 - (1/k - 1/[k(k+1)])

thus the next line (in the proof) means
2 - (1/k - 1/[k(k+1)]) < 2 - [ 1/k - 1/(k+1)^2] and so on

 

[coca cola]

thus the next line (in the proof) means
2 - (1/k - 1/[k(k+1)]) < 2 - [ 1/k - 1/(k+1)^2] and so on

hi steve.

but this is what i don't get. shouldn't it be the other way around, since for 2> or = k, 2 - (1/k - 1/[k(k+1)]) > 2 - [ 1/k - 1/(k+1)^2].

 

[steverulz55]

ah i see what you mean - didnt really check the proof haha

hmmm quite strange... his proof is quite all over the place haha - the inequality signs are wrong..probably a printing error?

 

[turtle_2468]

hi steve.

but this is what i don't get. shouldn't it be the other way around, since for 2> or = k, 2 - (1/k - 1/[k(k+1)]) > 2 - [ 1/k - 1/(k+1)^2].

I'd like to help but I have no idea of what the proof is..

 

[coca cola]

ahh thanks man. so it is wrong, ok so if you flip line two with three i.e.:

1 + 1/4 + 1/9... 1/k^2 + 1/(k+1)^2 < 2 - 1/k + 1/(k+1)^2

= 2 - [ 1/k - 1/(k+1)^2]

< 2 - (1/k - 1/[k(k+1)])

should be right eh?

umm, this geha really confuses me sometimes

turtle: its in the 50 tips book if you have, but surely 2 - (1/k - 1/[k(k+1)]) < 2 - [ 1/k - 1/(k+1)^2], for k = or > 2, is wrong as geha writes it and should be other way around 2 - (1/k - 1/[k(k+1)]) > 2 - [ 1/k - 1/(k+1)^2]. just substitute any value in or expand the thing.

edit: oh yea it should replace equals sign with < too.

 

[steverulz55]

the first and third line are the same in his proof and he went and wrote those were <

LOL =/

his book isnt that bad, but i think his steps in maths inductions are a bit brief...

 

[turtle_2468]

yep, sounds wrong to me too..

 

[coca cola]

yeah i know what you mean. it has some really good questions that are tricky and not covered by most other books but they are not really explained properly.

hey give me some more help, this is from geha's book as well for tip no.46, i don't get this part:

using: bc + ac + ab >or= a^2 + b^2 + c^2

how do you get this: (bc)^2 + (ac)^2 + (ab)^2 >or= bca^2 + acb^2 + abc^2

can you just times each terms individually like that, if you know what i mean? this does not seem obvious to me, any explaination of why?

 

[ngai]

using: bc + ac + ab >or= a^2 + b^2 + c^2

that sounds wrong....very wrong
sure its not ab+bc+ca <= a^2 + b^2 + c^2?

anyway, if u use my one:
ab+bc+ca <= a^2 + b^2 + c^2
let a = AB, b = BC, c = CA
and see wat u get

 

[coca cola]

oh ok, mistake sorry... let me see if i try that with the parameters you gave.