Sequence Definition and 1000 Threads

$\text{write the formula for the sequence}$ $\text{.24 }$ $$a_n=\frac{n^{n+1}}{5^{n+1}}$$ $\text{.25 }$ $$a_n=\frac{(-1)^{n}+1}{2}$$ $\text{26.}?$

Hey, I have some questions regarding zero sequence current flow in a multi phase system I was hoping some kind soul could help me with. Imagine the following scenario illustrated in my bad paint drawing below: A delta-wye(n) transformer are supplying a non linear load producing 3rd harmonics...

Take the sequence 1,2,3,4,5,6,7,8,9,10... If you found the percent change for each interval and kept on finding the percent change of the percent change of the sequence, why does the change become more and more chaotic? Here is a quick table I made...

Write out the first four terms of the sequence defined by the recursion n_(n+1)=n_1+1,n_1=−1 $\text{Write out the first four terms of the sequence defined by the recursion}$ $$\displaystyle a_{n+1}=a_1+1,a_1=−1$$. $\text{so then}$ $$\displaystyle a_{0+1}=-1+0=-1$$ $\text{stuck!}$

Hello everyone, I have an issue solving the following problem: You're on a mathematical Olympiad, there are m medals and it lasts for n days. First day committee gives U_{1}=1+\frac{1}{7}(m-1) medals. On the second day U_{2}=2+\frac{1}{7}(m-2-U_{1}) medals, and so on... On the last day...

Homework Statement 6 /(12 + 1), 1/(22 + 1),6/(32 + 1),1/(42 + 1) Homework Equations none The Attempt at a Solution I suspect this is not that hard, I get the denominators but the numerator alternates so I though I would need 6 to be the base of a power that alternates between 0 and 1 but I...

I'm using the book of Jerome Keisler: Elementary calculus an infinitesimal approach. I have trouble understanding the proof of the following theorem. I'm not sure what it means. Theorem: "An increasing sequence <Sn> either converges or diverges to infinity." Proof: Let T be the set of all real...

$\displaystyle s_n=\left(\frac1n-1\right)^n$ My attempt: For large $n$, the sequence oscillates between $e^{-1}$ and $-e^{-1}$ and therefore diverges. Now for the proof. Assume, for the sake of argument, that the sequence converges to $L$. $\exists N\in\mathbb{N}$ such that $|s_n-L|<0.1$...

If all main sequence stars are engaged only in hydrogen fusion, why don't they all exhibit the same color?

I am studying Classical Analysis with Marsden book. At very first chapter it covers sequence, field, etc... The book has theorems 1."Let F be an ordered field. We say that the monotone sequence property if every monotone increasing sequence bounded above converges." 2."An ordered field is said...

I am trying to up my understanding on Manifolds, Tensors and Forms by reading a book of that title by Paul Renteln. I have got stuck fairly early on by his use of "exact sequences". Can some one give me a concrete example of a shot exact sequence of the form 0 -> U->V->W->0 where U,V,W are...

If $\{x_n\}_{n \ge 1}$ is real sequence and $\limsup\limits_{n \to \infty} \frac{1}{n} \log |x_{n+1}-x_n|<0$, prove that $\{x_n\}$ is Cauchy sequence. My work: Let $a=\limsup\limits_{n \to \infty} \frac{1}{n} \log |x_{n+1}-x_n| <0$. Then, for every $\varepsilon >0$ there exist $N \in...

Homework Statement "For the given series, write formulas for the sequences an , Sn, Rn and find the limit as n->∞ (if it exists) Homework Equations ∑∞1 ((1/n) - 1/(n+1) The Attempt at a Solution I know how to take the limit, that's no problem. I'm a bit confused about what an , Sn, Rn are...

need a hand with a revision question, I don't quite understand how to go about solving it question is attached below

Hi, I have following two parameters with me a) Maximum three phase fault current in amperes (A) and phase angle in degrees (B). I want to calculate the positive sequence resistance (R) and reactance (X) from above two variables for a symmetric system. I couldn't figure out a way to find R and...

If we seek a bijection $$\wedge^p V \to \wedge^{n-p} V$$ for some inner product space ##V##, we might think of starting with the unit ##n##-vector and removing dimensions associated with the original vector in ##\wedge^p V ##. Might this be expressed as a sequence of steps by some binary...

The definition of a limit of a sequence, if the limit is finite, is: lim n >infinity un (un is a sequence) = l <=> ∀ε> 0, ∃N: n > N => |un - l| < ε This just means that un for n > N has to be a number for which: l -ε < un < l + ε Now, I'm wondering, can't we just say: n > N => |un -l| <...

Homework Statement Homework Equations a) the one given b) det(A-λI) = 0 find λ values using A c)use λ values to find eigenvectors The Attempt at a Solution This wasn't explained well enough so I can understand it in class. So far, I made the matrix being multiplied to A have the following...

Say we have a periodic sequencs, ABCDABCDABCDA... etc. We would normally call A term 1, B term 2, C term 3, etc. However, to find the nth term, do we need to designate A as term 0, B as term 1, etc? Since we would use n mod 4 to find the nth term, wouldn't this mean that 4, 8, 12, etc would have...

I have this series: $$\sum_{k = 1}^{\infty} {4}^{\frac{1}{k}}$$ To solve this, I am trying to compare it to this series $$\sum_{k = 1}^{\infty} {4}^{k}$$ So, I can let $a_k = {4}^{\frac{1}{k}} $ and $b_k = {4}^{k}$ These seem to be both positive series and $ 0 \le a_k \le b_k$ Therefore...

I have $$\sum_{n = 2}^{\infty} \frac{{(\ln\left({n}\right)})^{12}}{n^{\frac{9}{8}}}$$ We can compare it to $ \frac{1}{{n}^{\frac{1}{8}}}$. $ \sum_{n = 1}^{\infty} \frac{1}{{n}^{\frac{1}{8}}}$ diverges because $p < 1$ in this case. So, if I can prove that $...

ok I noticed that $$n \ge 0$$ so we have all positive numbers and with increasing values of $$n$$ this will go converge to zero I can only show this by looking at a graph of the the expression. apparently the expression would have to rewritten to take the limit?

If I have this sequence $$a_n = \ln\left({\frac{n}{n^2 + 1}}\right)$$ I need to find: $$ \lim_{{n}\to{\infty}} \ln\left({\frac{n}{n^2 + 1}}\right)$$ Shouldn't I be able to find the limit of$$ \lim_{{n}\to{\infty}} \frac{n}{n^2 + 1}$$ (which is $0$) and then substitute the result of that...

I have this sequence: $${a}_{n} = \ln \left(\frac{12n + 2}{-9 + 4n}\right)$$ I need to find the limit of this sequence. How can I go about this? Do I need to apply L'Hopitals rule? I'm unsure how to simplify this expression. If I use the rule $\ln(\frac{a}{b}) = \ln a - \ln b$ I get $\infty -...

When an alternator is supplied with a 3-phase voltage and its rotor is rotated in opposite direction to that of the stator rmf, the ratio phase voltage/phase current is the negative sequence impedance of the alternator. My understanding of this is as follows: When rotor is rotated in opposite...

Does the sequence \{f_n\}=\{\cos{(2nt)}\} converge or diverge in Banach space C(-1,1) endowed with the sup-norm ||f||_{\infty} = \text{sup}_{t\in (-1,1)}|f(t)| ? At first glance my intuition is that this sequence should diverge because cosine is a period function. But how to really prove...

I'm trying to understand a 3 phase induction machine model used as a generator in a Doubly Fed Induction Generator (DFIG) arrangement in Simulink. In this model for the induction generator component, they have stated that the model is a "Positive sequence model" of the induction generator...

Hello, It seems like mostly, the masters degree is skipped for those who are seeking a Phd degree (from Bachelor's to Phd directly). I'm in my fourth year as undergraduate, studying physics. I like both math and physics and I really want to master them both. The thing is that my university...

Homework Statement From the picture below, calculate the net resistance between points A and B if ##R_1=12## ##R_2=3.75## Homework Equations 3. The Attempt at a Solution [/B] I cannot think of any way but to find the equivalent resistance od ##R_1## and ##R_2## and add them up but since there...

Homework Statement A 25 year old programme for building new houses began in Core Town in the year 1986 and finished in 2010. The number of houses built each year form an arithmetic sequence. Given that 238 houses were built in 2000 and 108 in 2010, find the number of houses built in 1986...

Hey! :o Let $R$ be a commutative ring with unit. We have that if the sequences $0\rightarrow A\rightarrow B\overset{f}{\rightarrow}C\rightarrow 0$ and $0\rightarrow C\overset{g}{\rightarrow}D\rightarrow E\rightarrow 0$ are exact, then the sequence $0\rightarrow B\overset{gf}{\rightarrow}...

We recently performed one experiment regarding measurement of negative sequence impedance of an alternator(unloaded) in our lab session. The alternator was star connected and we shorted Y and B phases together, leaving R phase open(an L-L fault). How does this arrangement generate negative...

Find the $18th$ term in the sequence: $$\frac{1}{2},1,2 $$ $$a_1= \frac{1}{2}\ \ \ \ n=18\ \ \ \ r=2 $$ $$a_n=a_1\cdot r^{n-1}=131072$$

Homework Statement define calculation for the numbers ( a ; b; c) such that the new triplet is as follows. (a ; b ; c) --> transforms into --> (b+c ; c+a ; a+b) the first terms for a,b,c are : (1 ; 3 ; 5) Perform the calculation 2015 times, such that the new resulting numbers of the triplet...

Homework Statement Hi, I want to generate probing sequence using quadratinc probing technique. If j =4 & table size = 19 & assuming h(K) = 9. Homework Equations h(K), h(K) + 1, h(k) -1, h(k) + 4, h(K) - 4, ... h(K) + (TSIZE -1)power 2 / 4, h(k) - (TSIZE -1) power 2 /4 all divided modulo TSize...

Homework Statement Determine which of the sequences converge or diverge. Find the limit of the convergent sequences. 1) {asubn}= [((n^2) + (-1)^n)] / [(4n^2)] Homework Equations [/B] a1=first term, a2=second term...an= nth term The Attempt at a Solution a) So I found the first couple of...

Find the 79th term in the sequence - 7, - 4, - 1 $$a_n=a_1+\left(a_n-1 \right)d$$ $$n=79,\ \ a_1=-7, \ \ d=-3$$ $$a_{79}=-7+\left(79-1\right)\left(3\right)=227$$ I just followed an example?

Homework Statement Let (an)n≥1 be a sequence with a1≥0 and an+1=an(an+4), n≥1. Compute limn→∞ (an)(1/(2n)). Homework Equations a1≥0 an+1=an(an+4), n≥1 L = limn→∞ (an)(1/(2n)) The Attempt at a Solution Firstly, I had tried to see if an can be expressed only in terms of a1, but I couldn't get...

A sequence {$a_n$},$S_n=a_1+a_2+-----+a_n$,for each $n\in N, a_n>0$ if $2S_n=a_n+\dfrac {1}{a_n}$ please find $a_n=?$ (express in $n$)

*I am struggling with arithmetic and geometric sequences. if the 4th term is m-8, 6th term 8m+3 and 8th term is 10m-5 Calculate the 1st and 5th term Which term will have a value of -70The 4th term of geometric sequence is -16 and the 6th term is -64. Calculate the 3rd and 5th terms. thank you...

Hello! So let's say that you have a sequence ##a{_n}## and the limit as ##n->{\infty}## gives the finite number ##b## not equal to zero. If ##a{_n}## is known to be irrational, and ##a{_n}{_+}{_1}## can be shown to be irrational, does it follow by induction that ##b## is irrational? Is there any...

Hi, I can derive a few properties of the limit inferior and limit superior of a sequence of sets but I have trouble in understanding what they actually mean. However, my understand of lim inf and lim sup of a sequence isn't all that bad. Is there a way to understand them intuitively (something...

Dear Sir, Assuming that my lottery machine can generate 10 numbers (0..9), in which 0 and 9 are supposed to be starting and ending states of my Markov chain. I apply Markov chain to model each number appearance because I would want to modify the random generation process into, say, my own...

Homework Statement [/B] Find the limit as ##n \to \infty ## of ##U_n(a) =\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & a/n \\ 0 & -a/n & 1 \end{pmatrix}^n##, for any real ##a##. Homework EquationsThe Attempt at a Solution I find ##U =\begin{pmatrix} 1 & 0 & 0 \\ 0 & \cos a & \sin a \\ 0 & -\sin a &...

Homework Statement [/B] Use the Bounded Monotonic Sequence Theorem to prove that the sequence: \{a_{i} \} = \Big\{ i - \sqrt{i^{2}+1} \Big\} Is convergent.Homework EquationsThe Attempt at a Solution [/B] I've shown that it has an upper bound and is monotonic increasing, however it is to...

In my book, applied analysis by john hunter it gives me a strange way of stating an infinite sum that I'm still trying to understand because in my calculus books it was never described this way. It says: We can use the definition of the convergence of a sequence to define the sum of an...

Homework Statement given a geometric sequence sin(x),sin(2x), . . . c) find for which values of x∈(0,π) this sequence converges and calculate its limit Homework Equations |q|<1 or -1<q<1The Attempt at a Solution Ok so in part a) and b) i calculated the quotient and found out that...

I feel like this could go in quite a few of the Physics subforums (Quantum Physics, Beyond the Standard Model, Special and General Relativity, or High Energy, Nuclear, Particle Physics) instead of Astronomy and Cosmology, but hopefully this will work. This is my first question I've posed here...

In the attached picture, how is it justified to factor out an 'i' in the exponent of the 2 and the 5?

Homework Statement Consider the sequence given by b_{n} = n - \sqrt{n^{2} + 2n}. Taking (1/n) \rightarrow 0 as given, and using both the Algebraic Limit Theorem and the result in Exercise 2.3.1 (That if (x_n) \rightarrow 0 show that (\sqrt{x_n}) \rightarrow 0), show \lim b_{n} exists and find...