Just a simple question

Narciss:

lim(3/4)^(n-1) = ?
n->inf.

Hi Narciss,
I can 'see' that the answer is 0.
This is because 4 to the power of some huge number is going to be much bigger than 3 to the power of the same huge number, and as that number gets even bigger the difference will become more and more extreme.

Firstly, I must stress my English could be difficult to understand to a certain extent when it comes to math. It's only my second language and my classes haven't covered the math area just yet I'll be using (?) when I'm not sure if the term I'm using is correct.

Yes, I'd say the same. I've just sat my math test and we had to figure out something like this: lim(x->inf.) ((1-3/4+9/16-27/64..)*n^2)/(n^2-1))
It's looks a bit tricky here on the computer so it might be helpful to write it down by hand. You may notice the first inner parentheses (1-3/4..) is actually an infinite alternating geometric series(?) (or sequence(?). As much as I understand it, one has to determine the general(?) equation (an = a1 * q^(n-1)) and then place it instead of what is in the parentheses. So, I 'figure' the general(?) equation is -(3/4)^(n-1), since the the first term(?) a1 = 1 and the common ratio(?) q = -3/4. Having done this, one can then operate (or calculate or..?) with the limit(?) and, if did it correctly, the result is lim(x->inf.) (3/4)^(n-1) = 0.

Please correct me if I'm wrong, any help will be appreciated.

And of course I meant lim (n->inf.) and not (x->inf.).

hi Narciss,
It is really nice to interact with you in real time.

lim(x->inf.) ((1-3/4+9/16-27/64..)*n^2)/(n^2-1))

Firstly, shouldn't it be n->inf because there are no x's in the expression?

Also I am struggling a little with this (1-3/4+9/16-27/64..) if the dots mean that it goes on for ever no matter what x (or n) is, then, it is the infinite sum of a geometric progression
which is T ₁/(1-r) = 1 / (1- (-3/4)) = 4/7

or is it really meant to be (1-3/4+9/16-27/64....(-3/4) ^(n-1)) in which case it would be the sum of a geoopmetric progression

Sn = T ₁(1-r ⁿ)/(1-r) = 1(1-(-3/4) ⁿ)/ (1- (-3/4)) = (1-(-0.75) ⁿ)* (4/7)

You are right this poor maths presentation is making it difficult. I can write it up properly in maths speak (Latex) and import it if we decide it is really necessary but it does take quite a while and it is late in Australia so I am not over keen at present.

Anyway, would you like to comment on the 2 possible interpretations of the sequence. Which one do you want?

What do you think of this answer?
131219 latex limit question.JPG

Second interpretation, which now I think about it is the same thing (as n approaches infinity) so it is a good thing that I got the same answer.
131219 latex limit question2.JPG

What is your first language and where are you from Narciss?
You don't have to answer of course but I am always interested in where people live.
I am in Sydney, Australia. I used to teach at an international college and I really loved it.

Od dear.. you have indeed explained everything and corrected my mistakes. Your first interpretation is right, it is (or was in my test) the infinite sum of geometric progression. I probably confused you by using the wrong formula (or equation(?)) (an = a1 * q^(n-1)), which applies, in fact, to the finite(?) sum of geometric progression. I trully hope I'm putting this correctly heh. So of course I should have used the S = T1/(1-r) = 1 / (1- (-3/4)) = 4/7 and get the same answer as you.
I can only hope my maths professor is going to be 'reasonable' and give me 3 points out of 4, since I've obviously known how to do everything else and I just messed up the formulas. Eh, I'll see.

Thank you very much for your help, I really appreciate your effort.
I'm trully sorry for replying so late, I forgot about this a bit because I have to study for another class. And it is, how convenient heh, my first language class. Slovenian. Doubt you've ever heard of it, though.

I know exactly where Slovenia is. Are you from Ljubljana?. I love to play geography games so I know where lots of places are.
I just read your post again. Are you actually from Slovenia or are you just learning Slovenian?

Yes, I was born and live in Slovenia. Slovenian is my mother language. I've been spared the difficulties of learning it as any other than first language. Frankly, it is said to be one of the most complex languages to learn. English has a vastly rich vocabulary, although some Slovenian writers believe Slovenian can compare to English, whereas Slovenian has an equally rich grammar.

But I'm studying literature and it's development right now and I can honestly say it frightens me even more than grammar. The latter is at least logical and rational.

Well, I like things which can only be interpreted in one way, like math heh.

Yes, I am not a language person at all. I only speak English and when i was at school English was my worst subject. I am always astonished that students (like the ones at the international college and like yourself) can study difficult subjects in a foreign language. I don't think I ever could have done that!
I have never really studied grammar but I do think i would find it easier than other facets of language because there are at least rules that can be followed.
I think it would be easier to learn another language if you first formally understood the grammar of your own language. I think that would give you a starting point for comparisons.
As I said, I don't speak another language so this could all be nonsense.
I have had fun chatting and working with you on this question. If you want to chat more, that would be nice.
Thanks.
Melody

I certainly would like to chat, but how? Also probably not yet today because I have to be up the whole night and study, so I'll probably sleep through the whole afternoon (which will be in about 14 hours here). But after all that, I'd love to.

I hope that all your study pays off well.

You don't need to do anything now. Maybe you will do it when all your exams are finished. I certainly don't want to put more pressure on you.

Try joining up properly and then you can send me a private message. If I receive one I will respond quickly.
In the past this has not worked for me. I have received some messages but I don't think that the messages I send ever leave my outbox.
Anyway I would like to see if I can reach you that way.

Thanks
Melody.