Read about partial fraction decomposition | 8 Discussions | Page 1

  1. Ryaners

    Finding sum of infinite series

    [Please excuse the screengrabs of the fomulae - I'll get around to learning TeX someday!] 1. Homework Statement Find the sum of this series (answer included - not the one I'm getting) The Attempt at a Solution So I'm trying to sum this series as a telescoping sum. I decomposed the fraction...
  2. defaultusername

    Breakdown of a Logistic Equation

    Homework Statement I feel so stuck. Given the Logistic Equation: $$\frac{dP}{dt}=kP(1-\frac{P}{A})$$ a.). Find the equilibrium solutions by setting $$\frac{dP}{dt}=0$$ and solving for P. b.). The equation is separable. Separate it and write the separated form of the equation. c.). Use partial...
  3. D

    Partial fraction decomposition exercise 2

    Homework Statement Hello! Here is my second post on the subject partial fraction decomposition. The subject looks pretty easy to learn, but when I try exercises, I do not get to the correct answer. Please, take a look at the exercise below and help me to see my mistakes. Homework Equations...
  4. D

    Partial fraction decomposition using matrix

    Homework Statement Hello! I am doing a chapter on partial fraction decomposition, and it seems I do not understand it correctly. Here is the exercise doing which I get wrong answers. Please, take a look at the way I proceed and, please, let me know what is wrong in my understanding. Homework...
  5. yuming

    Telescopic sum issues, cant get Sk

    1. Homework Statement Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges Homework Equations 3/(1*2*3) + 3,/(2*3*4) + 3/(3*4*5) +......+ 3/n(n+1)(n+2) The Attempt at a Solution the first try, i tried using partial fraction which...
  6. O

    Definite integral involving partial fractions

    Homework Statement Homework Equations trigonometric identities The Attempt at a Solution I did a trig substitution of u=tan(θ/2) and from that I could substitute cos(θ) = 1-u2/1+u2 dθ = 2/(1+u2) du = 1/2 sec2(θ/2) dθ I simplified a bit and changed the bounds to get 2du/(5u2 + 1)(1 + u2)2...
  7. J

    Very long Taylor expansion/partial fraction decomposition

    Homework Statement I want to express the following expression in its Taylor expansion about x = 0: $$ F(x) = \frac{x^{15}}{(1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)} $$ The Attempt at a Solution First I tried to rewrite the function in partial fractions (its been quite a while since I've last...
  8. StrangeCharm

    Integration by Partial Fractions Help

    Homework Statement ∫ [x^(3)+4] / [x^(2)+4] dx Homework Equations N/A The Attempt at a Solution I know that the fraction is improper, so I used long division to rewrite it as x+(-4x+4)/[x^(2)+4]. Given the form S(x)+R(x)/Q(x), Q(x) is a distinct irreducible quadratic factor [x^(2)+4]. I used...
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