# absolutely

1. ### Show that an Infinite Series is (absolutely) Convergent

Hello, New to this topic after missing it at uni due to sickness! Would anyone be able to help me to do this question as im not really sure how to prove that something is convergent for all values of X. [I do understand how to show that a series converges for a certain value of X]
2. ### Converge absolutely?

For this problem I've tried doing the ratio test but it turns into a big mess and a pain to take the limit of, is there any way to simplify this type of problem? I already know the answer is B but proofing it is the hard part.
3. ### Is this series Absolutely Convergent?

Hello, I have the series \sum_{x=1}^{\infty} (-1)^2 \cdot \frac{arctan(x)}{x^2} and I am trying to determine whether it is absolutely convergent or divergent. By the ratio test: \lim_{n\to\infty} \frac{arctan(x+1)}{(x+1)^2} \cdot \frac{x^2}{arctan(x)} \lim_{n\to\infty}...
4. ### Deduce if the series converges absolutely or conditionally.

Σ (-1)^k * 3^k(k!)^2/(2k)! I use ratio test. |(3^k+1(k+1)!^2/(2(k+1)!/3^k(k!)^2/(2k)!| which after simplifying got me 3(k+1)^2/(2k+2)(2k+1) how does one show it converges absolutely?
5. ### Deduce if the series converges absolutely or conditionally.

Σ (-1)^k *(k^2+3k)/(k^3+k+2) I use absolute value theorem and then comparison test. k^2+3k/k^3+k+2 ÷ 1/k = k(k^2+3k)/(k^3+k+2) = 1/k this diverges by p series yet how does one find how it converges conditionally?
6. ### Fourier series absolutely convergence

Let f be a continuous function on circle [0,1]. Suppose its Fourier coefficients satisfy an are non-negative for all n. Show the Fourier series converges absolutely.(Hint, the sum of a positive series equals its Cesaro sum) My sketch of proof: since an are non-negative, Σ|an|=|Σan|=|(δn f)(x)|...

Here's the current scenario: Our current math teacher has a student teacher this year. He's absolutely awful at teaching. He's been teaching the rotation of conic sections unit and pretty much NO ONE understands what's going on. He teaches it with the assumption that we all have learned conics...
8. ### determine if the series is absolutely convergent, conditionally convergent or diverge

I need help to solve these questions
9. ### Absolutely Converges, but why?

((-1)ne1/n)/n3 converges absolutely apparently, but I don't see how. When I applied the ratio test, it came out to be one, but obviously that is incorrect. Here is what I did: | [((-1)n+1 e1/n+1)/(n+1)3] * [n3/(-1)n e1/n] | = | [n3/(n+1)3] * [e1/n+1/e1/n] | = 1, as n -> infinity
10. ### Is the following series absolutely convergent or not

Hi, The series is : \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{2n+1} The absolut series is : \sum_{n=1}^{\infty} \frac{1}{2n+1} But I'm stuck at this very (easy ?) step : s_{n} = \frac{1}{3} + \frac{1}{5} + \frac{1}{7} + ... But I can't determine, in my head, if it is convergent or not. I feel...
11. ### F not absolutely continuous

I have the following function F:[0,1]\to[0,1] (it is a distr. function. Not so important) It satisfies F(x) = 1/2 for x\in [1/4,3/4] F(1-x) = 1-F(x) for all x F(x)= 2F(x/4) for x\in [0,1/4] I want to show F is not absolutely continuous w.r.t. Lebesgue...
12. ### determining whether a series converges absolutely

Determine whether the series (-1)k-11/3k2+2k+1 converges absolutely, converges conditionally, or diverges. (and the summation goes to infinity and starts at k=1).
13. ### Need help with these math questions! It is due in 5 hours and I am absolutely stumped

Need help with these math questions. 1. Picture of histogram: https://oli.cmu.edu/repository/webcontent/65c2161c80020ca601c3920394e15386/m2_summarizing_data/topic_2_2/webcontent/Checkpoint2.2FINALMS/image2.png The questions are: For the above histogram, which estimates of the mean and median...
14. ### Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

Given the infinite series xn is absolutely convergent, show that the infinite series xn/(1+xn) is absolutely convergent. I am completely stumped, I have tried using properties of the limit test and the comparison test to show this, but I can't seem to make any progress,
15. ### Show that a series converges absolutely given convergence of two related series

Show that if \sum_{n=1}^{\infty}a_n^2 and \sum_{n=1}^{\infty}b_n^2 are convergent then \sum_{n=1}^{\infty}a_nb_n is absolutely convergent. Hint: Show |xy| <= 1/2(|x|^2 + |y|^2) for any x,y ε R I can prove the Hint - |xy|\leq 1/2(|x|^2 + |y|^2) 2|xy| \leq |x|^2 + |y|^2 |x|^2 + |y|^2 - 2|xy|...
16. ### Weak convergence of absolutely continuous probability measures

Hi there, Suppose I have a sequence of probability measures P_n which converges weakly to a probability measure P. Then we know that \lim_{n}P_n(A) = P(A) if A is a P-continuity set. Is it true that if, in addition we know that each P_n and P are absolutely continuous, then...
17. ### Absolutely clueless...

Ok guys i am not only new to these forums, attop of that when it comes to math in general, i am as clueless as a monkey trying to drive a plain... I do however need answere two 2 question, i need these answeres befor tommorow if possible, BUT the answere is not al i am seeking for, as a...
18. ### example of absolutely continuity

I'm studying Real analysis, It's known Lipschitz continuity implies absolutely continuity. and Cantor function is an example for uniformly continuous function but not a absolutely continuous function, i wonder if in between case, if f(x) is a holder continuous which is uniformly...
19. ### Absolutely or conditional convergence

is this series Absolutely or conditional convergent [k^(1/2)sin(k)]/(k^2)
20. ### Does a series converge if it's absolutely convergent?

A stupid one... (just to be sure) If I have a series that is converge absolutely so the series is converges? (it is implies from Cauchy criterion?) Thanks!