Sequences Definition and 590 Threads

How would you go on proving the following conjecture? Given S_0 = 0, \quad S_1 = 1, \quad S_n = a S_{n-1} + b S_{n-2} Prove that { S_n }^2 - S_{n-1} S_{n+1} = (-b)^{n-1} \quad (n = 1, 2, 3, ...)

Homework Statement Determine whether the sequences are increasing, decreasing, or not monotonic. 1) an= \frac{\sqrt{n+2}}{4n+2} 2) an=\frac{1}{4n+2} 3) an=\frac{cosn}{2^{n}} 4) an=\frac{n-2}{n+2} Homework Equations The Attempt at a Solution I thought that the number 1 and 2 were...

Homework Statement Determine whether the following sequence, whose nth term is given, converges or diverges. Find the limit of each convergent one. n[1 - cos(2/n)] Homework Equations I have made a solid attempt and obtained an answer but I am convinced I made a mistake and have missed...

I was looking at some practice tests and I came upon this tricky question. I'm not sure I would have got it on an exam! Consider the set, S, of all infinite sequences whose entries are either 1 or 2. However, if the nth term is 2 then the n+1th term is 1. I.e every 2 is followed by a one...

I am trying to remember the formulas and ways to do this but I am have much trouble! Please help! Thank you! 1) Find the sum of the first 50 terms 1, 8, 15,... using the sum of an arithmetic series formula. 2) Find the sum of the n terms of the arithmetic sequence a1 = 7, a12 = 29, n = 12.

define the sequence P_n as follows: P_{0} = 1 ; P_{1} = a and P_{n} = 6P_{(n-1)}-P_{(n-2)} + 2a^2-8a+4 Then each term is a product of two numbers as follows P_{n}= {1*1,1*a,a*b,b*c,c*d,d*e,\dots} where b = 2a-1 c = 4b-a d = 2c-b e = 4d-c f = 2e-d ... ... Has anyone come across...

I have already completed this calculus course but I can't seem to do these problems that I should know I have to find the limit of the sequence which seems to be the same as the limit of a function. Homework Statement Find the limit of the given sequence as n \rightarrow \infty...

I have been given 5 peptide chains with ER sequencs. I am supposed to draw the chain as it would be associated with the ER. But I don't understand by looking at one with just an N-terminal and Er signal how it should be positioned. How can you tell just by the presence (or absence of) an ER...

Ok so I am in Calculus II this summer and its pretty easy so far. However, I have heard the hardest part about Calc II is series and seqence. Why so? And what can I do to make it easier on myself? What was your expierence with sequence and series. Thanks in advance.

I wrote everything on the scanned image: http://img516.imageshack.us/img516/79/phprollyypmkz6.jpg The solution to the first sequence problem is 0, i.e. it converges, which is a puzzle to me... Ignore the limits in the second problem, all I need to know is how to integrate it. Thanks for any...

While a Fibonacci sequence is the sum of the previous two terms, what of sums of the preceeding n terms, and have such sequences (n > 2) been found to occur in the natural world?

Homework Statement Hi everyone. First time trying a forum let alone PhysicsForums.com, everyone seems very nice here. I am trying to figure out whether a sequence is convergent or not by writing out the first 5 terms. The sequence is: sin[1+(pi/n)]+nsin(pi/n). Homework Equations I...

Homework Statement 4.8 Show the following continuous theorem for sequences: if a_n \rightarrow L and f is a real valued function continuous at L, then bn = f(a_n) \rightarrow f(L). Homework Equations No real relevant equations here. Just good old proof I'm thinking. The Attempt at a Solution...

Homework Statement Does A subsequence of a sequence X converges to a point in I => The sequence X in I converges to a point in I ?The Attempt at a Solution I think yes because the subsequence is the sequence itself minus a few finite number of points. Since they both are in the same set I, I...

This was the extra credit question on a quiz I had today, I am very anxious to find out the answer. 1. Homework Statement Find the apparent Nth term of the sequence 2,-5,10,-17 ... n 2. Homework Equations Not sure really on this an = ... 3. The Attempt at a Solution...

A={xεR:X^11+2X^5<2} let a=supA By choosing a suitable sequence of elements of belonging to A and which tends to a as n->inf, or otherwise, show that a^11+2a^5=<2.Choose another sequence this time of all real numbers not belonging to A to show that a^11+2a^5>=2 and hence show that a^11+2a^5=2,so...

This is the sequence: 1, 2, 5, 14, 41, 122 1. Is this a geometric series or an arithmetic series? 2. I know the formula is a sub n=[3^(n-1)+1]/2, but how do you get that from a sub n=a sub 1 * r^(n-1), which is the geometric formula for series.

This is a very vague question, but I'd like to know whatever insights anyone could offer about exact sequences. What do they represent? Why are they so important? I'm studying homology right now, and exact sequences are central to the theory, but I've never seen them before. What is the...

Suppose I have a sequence a_0 = 1 a_n = \sum_{k=1}^n f(k)\cdot a_{n-k} where f(n) is a known function (in binomial coefficients, powers, and the like). In general, how would I go about proving that a_n\sim g(n)? I'm working on more closely estimating the function by calculating its...

I'm having a bit of trouble with two analysis questions, they are: 1) a_n -> a iff every subsequence of {a_n} converges to a 2) a_n->a iff {a_n} is bounded, and a is its only cluster point. For the first, I was thinking of doing something along the lines of saying that a subsequence of...

hello any one can help me with this question thanx (a) Find a recurrence relation for the number of n-digit sequences over the alphabet {0, 1, 2, 3, 4} with at least one 1 and the first 1 occurring before the first 0 (possibly no 0’s). (b) What are the initial conditions? (c)...

Homework Statement If p does not divide a, show that a_n=a^{p^{n}} is Cauchy in \mathbb{Q}_p. The Attempt at a Solution We can factor a^{p^{n+k}}-a^{p^n}=a^{p^n}(a^{p^{n+k}-1}-1). p doesn't divide a^{p^n} so somehow I must show that a^{p^{n+k}-1}-1 is divisible by larger and larger powers of...

Sequences and series - try again :) Hi, I'm going to try to post this question again, hopefully it is more clear this time. I'm not sure how to approach this question, or really, what this question is asking me! Homework Statement The k-th term of a series, Sk = a*[(1-(r^k))/(1-r)], is...

Homework Statement Hi, it's been a while since I've done questions such as the one below. Does anyone know how to solve it? (Note that k and n are actually sub-k and sub-n). Thanks in advance. The kth term of a series, Sk = a (1-R^k) / (1-R) , is the sum of the first k terms of the...

i need to show that there exists a class of sets A which is a subset of P(Q) such that it satisfies: 1) |A|=c (c is the cardinality of the reals) 2) for every A1,A2 which are different their intersection is finite (or empty). basically i think that i need to use something else iv'e proven...

i need to prove that there are c sqequences of rational numbers. basically, i need to show that |Q^N|=c. here, are a few attempts from my behalf: i thought that Q^N is a subset of R^N, so |Q^N|<=c, but this doesn't help here, so i thought perhaps to find a bijection from {0,1}^N to Q^N. i...

we have a sequence {a_n}, such that for every n natural, a_n>0 and it satisfies: lim (a_n*a_n+1)=1 prove/disprove: if {a_n} is bounded then {a_2n} converges. i haven't found any counter example, is this statement true or false, if is false then what's the counter example? p.s couldn't...

let f,g be continuous functions from R to R and suppose that f(x)=g(x) for all rational points. prove that f(x)=g(x) for all x in R. - i said that we know that since given any real number c, there exists a rational sequence (xn) such that xn converges to c, therefore we conclude that...

I was trying to do some heuristics with the Cramér model, but I wasn't able to find a good asymptotic for a certain quantity and I thought I'd see if anyone had something good. I did check a few sequences on the OEIS first, but I didn't notice anything there. Essentially, I'm looking to...

urgent! i need the proof of squeeze lemma on sequences if y_n \leq x_n \leq z_n and y_n \rightarrow p and z_n \rightarrow p then x_n \rightarrow p Note. I'm not looking for the proof of the regular squeeze theorem. this is supposed to be a proof adapting the proof of squeeze theorem onto...

We learned in class how to find the sum of any geometric sequence with the following formula: Let x = Sum Of Geometric Sequence; x = [Take mythical next term - real term]/(ratio - 1); The real term is the first term of the sequence and the mythical next term would be the next term for...

I am not too sure what to do to answer this question. Each year for the past 5 years the population of a certain country has increased by a steady rate of 2.7% per annum. The present population is 15.2 million. a) what was thepopulation 1 yr ago? b) what was the population 5 years ago? I...

Hi I have a problem with sequences and series. Can anybody help, please? The question is For the sequence U1, U2, U3, ...Un... the terms are related by Un = Un-1 +2Un-2 where n is greater or equal to 1, U1=2 and U2 =5. Find the values of U7, U11, and U14. Can someone...

i need help- arithmetic sequences There many arithmetic sequences which seventh term equals 5. prove all of them have the same sum of their first 13 elemnets. find the sum i found the sum was 65 but i don't know how to prove it.

For the geometric sequence with tn = 2(-1)^n*(1/3)^n (a) the sum of the first 99 terms (b) the sum of the odd-numbered terms t1 + t3 + t5 +...+ t99 (c) the sum of the even-numbered terms t2 + t4 + t6 +...+ t98 so do i first maybe want to convert that into something simpler? why would they...

Please help I have ALOT of questions! 1.)Starting at 888 and counting backward by 7, a student counts 888, 881 and 874, and so on. Which of the following numbers will be included? a) 35 b) 34 c) 33 d) 32 e) 31 Ok, so I by using the calcuator the aswer is 34, but how would you calcuate...

We're going to be starting them in a day or two, and I just wanted to know ahead of time what you guys might think we'll be learning with them, like formulae and that kind of stuff..

Hello. I know this: If (a_n) is a bounded below decreasing sequence, then lim (a_n) = inf { a_n / n = 1,... } n->oo How to translate this to real functions ? I mean, I have read that: lim (sup { f(x) / 0< |x-a|< e}) = e->0 inf { sup {f(x) / 0< |x-a|< e} / e >...

Hello, I'd like to define a sequence in mathematica and let it go, but I'm not sure how to tell mathematica to look for the previous number in sequence and then derive the new one. Something like this, a_1, a_2, a_3, a_4, a_5 = 3, 7, 23, 87, 343 = 0+3, 3+4, 7+16, 23+64, 87+256 where...

Hello, I'm looking for some quotes about sequences, fractals and chaos. Any kind of help is welcome. Thanks :)

Hello, It's rather a formal question, not asking for anything specific. I'm writing a pseudo-book for my math class, which should contain 1. arithemtic sequences 2. geometric sequences 3. fractals. And so here's my ask for help and a question, Do you know anything about any of these...

i have a few problems with sequences 1. show, that if: \lim_{n\to\infty}a_{n}=L than sequence: b_{n}=\frac{a_{1}+...+a_{n}}{n} is convergent to L 2. show that the sequencea_{n} is monotone, bounded and find out its limit, if: a_{1}=2 a_{n+1}=\frac{a_{n}+4}{2} 3. show that if the...

Just futzing around, this sequence was suprisingly patterned for the first 8 numbers, then became erratic: 1, 1, 3, 3, 9, 9, 15, 15, 17, 27, ? And for the sake of more fooling around, this one just popped into my head: 1, 2, 4, 6, 16, 18, 64, 66, 100, 112, ? DaveE

1. Give an example of an arithmetic sequence such that the 35th term is 4,207? I used the general form of an arithmetic seq. an = a1 + (n-1)d and found that, a1 = 25, and d = 123 Does this look ok? I had to use some trial and error since we have two unknowns.2. What is the 57th smallest whole...

hiw to solve for infinity sum (n=1) [sin n(pi)] / 6 ?? pls help...thanx

I've been reading the paper on Balanced Sequences and Optimal Routing (Altman, Gaujal, Hordijk; 2000). However, there are a couple of proofs given that I don't quite follow. There are statements made that are assumed to trivially follow, but I can't see how and am hoping someone will be able to...

I was wondering about this when it hit me, can a sequence ever be both arithmetic and geometric? I was thinking maybe a sequence like 0, 0, 0, 0... or 1, 1, 1, 1... where it's constant but I don't know thoroughly if there are any restrictions on arithmetic and geometric sequences that prohibit...

determine the following sequences converges 17n^54 + 1/n^2 +42 divide by n^55 + 75n^54... pls help...

Working from "Principles of Mathematical Analysis", by Walter Rudin I have gleaned the following definition of continuity of a function (which maps a subset one metric space into another): Suppose f:E\rightarrow Y, where \left( X, d_{X}\right) \mbox{ and } \left( Y, d_{Y}\right) are metric...

Need help clairfying some stuff. How do you determine if a Sequence is not monotonic? Also if its just inc. or dec. its monotonic? For example. Seq=An= 1/(2n+3) First 4 terms are {1/5,1/7,1/9,1/11,...} So its decreasing...and I guess monotonic? And how would you determine if that sequences...