Sequences Definition and 576 Threads

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 [SIZE="3"]a[SIZE="1"]n = ... 3. The...

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, S[SIZE="1"]k =...

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 :)

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...

I just can't get the following question. Can someone help me out? Q. Let a < a_1 < b_1 and define a_{n + 1} = \sqrt {a_n b_n } ,b_{n + 1} = \frac{{a_n + b_n }}{2} . a) Prove that a_n \le a_{n + 1} \le b_{n + 1} \le b_n for all n. b) Deduce that the sequences {a_n} and {b_n} both...

I have to use the partial fraction technique on 1/(4k^2 - 1)... ANSWER: So far so good and I get 1 / 2(2k-1) - 1 / 2(2k+1), is this correct? I now need to show that ? \sum 1 / 4k^2 - 1 = n / 2n + 1 Please help :confused:

For a sequence a_1, a_2, ... in R^n to be convergent there are (at least) 2 theorems, as follows: if for all epsilon>0 there exists an M such that when m>M, then |a_m-a|<epsilon and also: If u(epsilon) is a function such that u(epsilon)-->0 as epsilon-->0, then the sequence is...

my problem is regarding sequences: Sum first 20 terms of a=r^k-1 terms are 2, 4/3, 8/9,... and ratio is 2/3 and r < 1 so its an inflated series and 2(2/3)^19 = .009021859795 BUT it is an inflated series right? and my...

I think I'm having some trouble on this. First I'll state what the question is then I'll show what i have and my reasoning. Determine if the sequence{b sub(n)} is convergent by deciding on monotonicity and boundness. given: b sub(n)=n^2/2^n First I plugged in numbers for n starting with...

Does anyone know what are the uses of Sequences and Series in real life:confused:

Question Consider the sequence \{p^n\}_{n\in\mathbb{N}}. Prove that this sequence is Cauchy with respect to the p-adic metric on \mathbb{Q}. What is the limit of the sequence?

Let (x(n)) and (y(n)) be sequences of positive numbers such that lim(x(n)/y(n)) = 0. If lim(x(n)) = +∞, then lim(y(n)) = +∞ If (y(n)) is bounded, then lim(x(n)) = 0 To me this is self-evident. But HOW can it be proved?

Hey there everyone, We were discussing factorial sequences in my last pre-calculus class. Factorials are pretty cool. I asked if they had any rel world applications or examples I could put into my notes. She then told us if we could find an example that we'd get extra credit on our quiz, I'm...

I need to determine whether Sigma [sin(1/x)] for x=1 to x=infinity converges or diverges. I have a feeling that it diverges, but I don't know how to prove it. Thanks

hello all been workin on this problem: let An Bn and Cn be sequences satisfying An<=Bn<=Cn for all n an element of the natural numbers suppose that An->x and Cn->x, where x is a real number show that Bn->x this is how i did it A_n\le B_n\le C_n \forall n\epsilon N...

hello all I found this rather interesting suppose that a sequence {x_{n}} satisfies |x_{n+1}-x_{n}|<\frac{1}{n+1} \forall n\epsilon N how couldn't the sequence {x_{n}} not be cauchy? I tried to think of some examples to disprove it but i didnt achieve anything doing that, please...

Definition: Suppose T is an index set and for each t in T, X_t is a non-void set. Then the product \Pi_{t \in T}X_t is the collection of all "sequences" \{x_t\}_{t \in T} = \{x_t\} where x_t \in X_t. Does this mean that \Pi_{t\inT}X_t is the set containing all possible sequences defined by...

I wonder do the genes have the same exon-intron junction sequences or do they have different junction sequences? I was told that all genes have this general junction sequences of the exon-intron-exon: 5'---exon---A/CG-><-GUPuAGU----intron-----Py12NPyAG-><-G---exon---3' The arrows indicate...