1. L

    How to solve two series to figure it out the convergence / divergence

    Hello, guys! I have two series: \sum_{n=1}^{\infty}(-1)^{n}\dfrac{3n-1}{n^2 + n} My question is how to figure it out their convergence / divergence.
  2. A

    General Question about Convergence/Divergence Tests

    Hi guys! I'm here again with a general question that's been bothering me all day today as I study for my calc 2 exam which is primarily on tests: I'm taking Calculus 2 for Physics/Engineers as part of my course curriculum for getting a Bachelors in Chemistry and I'm doing well in understanding...
  3. A

    Generalized Mediant. New root approximating methods

    Allow me to introduce a very simple arithmetical operation: The Arithmonic Mean, which surprisingly and from the evidences at hand, has not been used in mathematics since ancient times up to now. I use the word 'Surprisingly', because it is a generalization of the 'Mediant' operation which is...
  4. N

    Series and Convergence Tests

    Hi Guys, I would like to ask one question about a multiple choices that I kept getting wrong. Can someone shed some light?
  5. K

    Sequence Convergence Proof

    Hi, I've been reading a book in order to prepare for a heavy on the proofs calculus course in the fall and have run into some trouble with the following proof Prove that the sequence $(a_n)$ given by $a_n = 3 - \frac{4}{n}$ $\forall n \in \mathbb{N}$ converges to 3. The final lines of the proof...
  6. R

    Interval of Convergence for differing odd/even coefficients of power series

    Hello, I am studying for a midterm this week. One of the practice problems is to find the radius of convergence of \sum_{n=0}^{\infty} a_n x^n where a_n = 5^n if n is odd and a_n = 1/3^n if n is even. It took me a while to hazard a guess that I take the smaller of the two radii? Then a =...
  7. H

    convergence of integral

    Investigate the convergence of the integral of ((sqr(2x/pi)-sin(x))^-1 from 1 to pi/2 thank's in advance
  8. V

    Indefinite integrals and convergence

    Can somebody confirm if this is correct and also i need a little help with the convergence. I think i need to fiind p=Alpha*something. Sorry for bad handwriting Imgur: The most awesome images on the Internet
  9. T

    Proving a Sequence's Convergence

    Hello, can you please check my work? Prove sin(n^2)/n^(1/3) converges to 0 Proof for any e > 0 abs(sin(n^2)/n^(1/3)) < e sin(n^2)/n^(1/3) < e Since the range of sin(n^2) is [-1,1], sin(n^2)/n^(1/3) < or = 1/n^(1/3) so let 1/n^(1/3) < e. So 1/n < e^3 let N < or = n Then, sin(n^2)^3/n < or =...
  10. X

    ratio test to test absolute convergence

    in this question , i tried to solve it using ratio test to determine whether it is absolutely convergent or not , unfortunealy , i keep on getting infinity/ infinity , what does it mean ? does it mean diverge absolutely or ration test is not suitable to test the series ? if it is diverge...
  11. B

    Interval of Convergence of Infinite Series

    Hi I have two questions asking me to find the interval of convergence of an infinite series: 1. Sum n=1 - infinity of: (2x)^n/(n^2+1); and 2. The Taylor series (or actually McLaurin series I think) for ln(1+x) about x=0 ie sum k=1 to infinity ((-1)^k*x^k)/k The actual words I have used are...
  12. S

    Series Convergence

    Please show me how to do this. I think three converges because you can compare it to the convergent p- series 1/n^2 correct? What about I and II?
  13. S

    Series Convergence

    Please help me figure out what I am doing wrong! (Headbang) Thanks!
  14. E

    Difficulty finding power series representation of a function

    As the title says, I'm having a lot of trouble finding a power series representation of a function. Here it is: And here's my attempt at a solution: I had a lot of trouble trying to reindex the summations such that I'd have a single summation at the end. This is what I ultimately got...
  15. H

    Improper Integral convergence

    While finding the Fourier Transform of the unit step function u(t) , I came across the following integral: \int_{0}^{\infty}e^{-i\omega t}dt = \left[-\frac{e^{-i\omega t}}{i \omega}\right]_{0}^{\infty} The textbook says that the integral will not converge.Can anyone explain the reason why so?
  16. H

    Finding the domain of absolute convergence

    Find the domain of absolute convergence for: $$\sum_{n=1}^\infty \frac{(n!)(iz+1)^n} {n^3+ \sqrt[3] {n}} $$ which test should be used in this case? I tried the ratio test, but the terms did not cancel out (some did): $\lim_{n\to \infty} \frac{(n+1)!(iz+1)^{n+1}} {(n+1)^3 + \sqrt[3]...
  17. X

    conditional convergence

    taking the notes as an example , we can see that series 9 is conditionally convergent , because it's converging by using alternating test . But , it doesnt converge absolutely question is can we call the series as conditionally convergent if a particular series doesnt converge by using...
  18. C

    Summation n = 1 to infinity (-1)^(n+1)*(2+(-1)^n)/n convergence or diverg.?

    Hello, I need to find out if summation n = 1 to infinity (-1)^(n+1)*(2+(-1)^n)/n is convergene or divergence. Lim n = 1 to infinity (n+1)*(2+(-1)^n)/n = 0, so we don't know for sure. What's the best way to check if it's convergence or divergence?
  19. A

    Convergence of a sequence?

    I have this sequence: And I have to see if it converges. I tried starting with proving this (based on the known convergence criterion for sequences): But I can't simplify that fraction ... I've been stuck for more than an hour busting my head. Excuse my english. Thanks for your time. EDIT...
  20. M

    Does sum in the Digamma function exist?

    I am reading about the Digamma function. It deduced in, that $$\psi(z)=-\gamma-\frac{1}{z}+\sum_{k=1}^{\infty}\left [ \frac{1}{k}-\frac{1}{z+k} \right ]=-\gamma+\sum_{k=0}^{\infty}\left [ \frac{z+1}{(k+1)(z+k)} \right ]$$ for all $z\in \mathbb{C}\setminus \{0,-1,-2,\cdots \}$, using the...