1. J

    Series Convergence

    What are the values of k that make the series convergent?
  2. 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.
  3. S

    Proof of a Sequence and serie

    Dear Ladies and Gentlements, My Prof. give me this mathematical problem and i have no clue to solve this problem. Maybe someone find a way. Task The series a0, a1, a2... is defined as this instruction: a0=1 and an = an-1 * ( 4 - (2/n)) for n>= 1 now i need to prove that for evey n>=1...
  4. V

    Fourier-Series, where is my mistake?

    Hello, I've got a piecewise defined, 4-periodic function . I have calculated the coefficients as seen in the pictures . The problem is, when I plot the Fourier series , it seems not to be correct, as you can see in this picture (blue: Fourier series, black: actual function): I am looking...
  5. E

    Half range cosine FS expansion

    Hi everyone, my university maths lecture notes suggest that in finding a fourier series expansion for a function it is easiest to find the even extension. As such, I mirrored the function across the y-axis (as shown in working link) and have been trying to solve it thusly, however piecewise...
  6. Q

    How to adjust this two series?

    Dear users, I'm struggling with a problem of fitting two series of numbers (I'm using Excel). Let's go: I have two series (A, B), consisting of several points recorded over time (a1, a2, a3...; b1, b2, b3...). Each series has different units (A="$", B="km"). I want to apply the formula...
  7. B

    Estimating integral using Taylor Series, extra term

    Hi I have a question to find the Taylor Series for y(x)=ln(1+x) up to and including terms of 0(x^5). I found that series to be: x - 1/2x^(2) + 1/3x^(3) - 1/4x^(4) + 1/5x^(5)...which may or may not be correct! The next part of the question asks: "Use the series to estimate the value of the...
  8. L

    Taylor series for cos(z) about z=pi/4 using Maclaurin series

    I want to express $\cos(z)$ in a Taylor series centred on $z_0=\frac{\pi}{4}$. Using the formula $\sum_{k=0}^{\infty} \dfrac{f^{(k)}(z_0)z^k}{k!} $ and the fact that $f^{(k)}(z)=\cos(z+\frac{k\pi}{2})$ in this case I found that the Taylor series is $$\sum_{k=0}^{\infty}...
  9. 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?
  10. N

    Show that function is periodic (Fourier series)

    Hi, I have the following problem: Assume that the function f is 2\pi-periodic and has the Fourier series: f(x) = a_0 + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) Let k \in \mathbb{N}. Show that the function g(x) = f(kx) is 2\pi-periodic, too. I am in general quite unsure how to start...
  11. L

    How to solver this Taylor series?

    1. We have function and and we have to find Taylor series for at and find the derivative at .
  12. U

    Taylor Series

    Use the definition to find the Taylor series (centered at c) for the function. f(x) = cos x, c = (pi/4) I have this one 3 times but to no avail.
  13. U

    Maclaurin Series

    Find the first 4 terms of the Maclaurin series for the given function. f(x) = (sin x)/(1 + x) Note: c = 0 I can find the first three terms but not the fourth term or any other terms after 3.
  14. L

    Taylor Series Expansion?

    Hi. I'm reading this one book about pulsatile flow and there's one passage in it that me and my friends can't make sense of (Headbang). You don't need much insight into the physical problem to understand it, so I figured I'd ask for help here. Also, the author probably used a Taylor series...
  15. H

    complex series

    Hi, I need to find the region where the following complex series converges: I computed the absolute value of the function and used the nth root test/Is it correct? if not,how can i find the region? Thank's in advance
  16. E

    Power Series Expansion

    Obtain the power series expansion of \frac { 3 }{ (1+x)(1-2x) } , giving the general term and radius of convergence.
  17. 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 =...
  18. A

    Squaring an Infinite Series

    How would I go about computing the square of a series of the form: \Sigma_{j=0}^{\infty}[B_jsin(\Omega_j)+C_jcos(\Omega_j)] I imagine this would involve a Cauchy product, but I'm not sure how to get started.
  19. K


    View image: analitik
  20. S

    A Series of Questions About Some Series: Primes, Waves, and Factors

    A Series of Questions About Some Series: Primes, Waves, and Factors Abstract A Trigonometric Series is crafted that gives the number of factors of x for all x. It is then manipulated to list all those factors. It is then used to give the exact distribution of the primes. It is then changed...