Recent content by Elysian

Pretty sure. To give you an overview of what I did, I took an and looked at an+12. Which gave a formula an2 + 2 + \frac{1}{ an+12}. I compared an2 to 2n, and said that an2 > 2n for n\geq3. Then by induction proved that this is the case for an+12 \geq 2(n+1). Then I had to find a value...

I did actually solve it, thank you for checking back. My bad on not replying. I found an upper and lower bound of the sequence, and with this I plugged in 200 into the lower bound of sqrt(2n), and the upper bound of sqrt(13n/6) and then got 20 and 20.866 respectively.

Yeah it is.

Homework Statement Define a1=1, and for every n>1, an+1 = an + \frac{1}{an}. Prove that 20 < a200 < 24The Attempt at a Solution I tried a few things to no avail. First, I showed that this is an increasing function by showing an+1 > an. I tried finding a limit, by saying if...

Ohh I think I get what you mean The upper bound for the LHS is 1, and the first term of the right hand side is 1 and then adding constants, so they can't be equal? There's only one intersection of their ranges so it doesn't work out then I guess?

Homework Statement Does the triple integral [SIZE="3"]\int^{1}_{0}\int^{1}_{0}\int^{1}_{0}\frac{1}{1+x^2 y^2 z^2} = \sum^{∞}_{n=0}\frac{1}{(2n+1)^3} Homework Equations The Attempt at a Solution I've not a single clue on what to do with this problem. I figured maybe I could find a...

Thanks, and yeah I get you, It's pretty much what I said in the last part of the question. What happens then if it is a zero mean? It holds but how would we go about proving that for zero means it is true but for nonzero means it isn't? I've just given you what was given to me so I don't believe...

Homework Statement Let f be a 2π-periodic function (can be any periodic really, not only 2π), and let g be a smooth function. Then lim_{n\rightarrow∞}\int^{B}_{A} f(nx)g(x) converges to \frac{1}{2π}\int^{2π}_{0}f(x) The Attempt at a Solution So far, I've come up with somewhat of...

Thanks but it doesn't really give me a decent method I can follow. Some of the methods make little sense to me

Homework Statement Prove that lim_{n \rightarrow ∞} \frac{n! e^{n}}{n^{n+\frac{1}{2}}} = \sqrt{2π}Homework EquationsThe Attempt at a Solution Alright so for this problem I noticed it looked kind of similar to the integral formula for a normal distribution from statistics with the...

Homework Statement Study the convergence of the following sequences a_{n} = \int^{1}_{0} \frac{x^{n}}{1+x^{2}} b_{n} = \int^{B}_{A} sin(nx)f(x) dx The Attempt at a Solution For the first one, I said it was convergent. I'm not exactly sure why though, my reasoning was...

It would equal 0. So as SammyS put it, it would be \displaystyle \int_{-\pi/2}^{\pi/2}\left(\frac{1}{1+e^{x}}-\frac{1}{2}\right)\cos(x)\,dx\ ?, where the first term would go to zero and then I'm left to evaluate the last bit which would be -\int_{-\pi/2}^{\pi/2}\frac{cos(x)}{2}? Is this just...

Oh jeez I forgot to put the interval. its from -pi/2 to pi/2. I'm really sorry about that

Homework Statement Find the integral of \int\frac{cos(x)}{1+e^{x}} Homework Equations Given that \frac{1}{1+e^{x}}-\frac{1}{2} is an odd function The Attempt at a Solution I tried integration by parts, with both u = cos(x) and u = 1+e^x, and both only complicated it even...

You're correct that I will incorporate computers into this. I'm mainly looking to model business scenarios, anything basic related to that. I have no preference for programming languages, if needed I can try and learn any ones that'd be required.