[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...
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...
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...
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...
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...
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...
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...
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...