Recent content by Perrault

Homework Statement Let S ⊆ R be such that (i) a, b ∈ S ⇒ ab, a + b ∈ S (ii) for all x ∈ R exactly one of the following holds x ∈ S, x = 0, −x ∈ S. Show that S = {x ∈ R ; x > 0} (the set of positive numbers P) 2. Relevant theorems (T1) a² > 0 ∀ a ∈ R. (So a²∈P) (T2) All positive...

Awesome guys, it worked! Thanks!

Of course, I missed something essential! The whole left side is squared. I edited the original post. Thanks for pointing that out.

Thanks for your response. By "n=1,2,3,...", the problem statement means the natural numbers. Sorry for the confusion. Also, induction is mandatory.

Show by induction that (2n-1)!/(2n)! <= 1/(3n+1) for all n Homework Statement Show by induction that (\frac{1\cdot3\cdot5\cdot\cdot\cdot(2n-1)}{2\cdot4\cdot6\cdot\cdot\cdot2n})^2 \leq\frac{1}{3n+1} for n=1,2,3, ... The Attempt at a Solution It might not really be relevant, but I've...

This is something trivial that has been bugging me for a while. When someone is far ahead of you on a sidewalk, you see their arms swinging and feet beating the ground. But how can you make out if they are walking towards or away from you? Suppose that I don't want to stand still for thirty...

Thanks LCKurtz, it worked :smile:

I'm sorry, I don't understand exactly what you are suggesting. How is ##(81 + (x-1))^\frac 1 4## any easier to expand than ##\sqrt[4]{80+x}##? Thanks for your help!

Homework Statement Use a series expansion to calculate L = \lim_{x\to\ 1}\frac{\sqrt[4]{80+x}-(3+\frac{(x-1)}{108})}{(x-1)^{2}} Homework Equations A function f(x)'s Taylor Series (if it exists) is equal to \sum_{n=0}^{\infty}\frac{f^{(n)}(x)}{n!}\cdot (x-a)^{n} Newton's binomial theorem...

Hello, and thanks for your replies, I have trouble understanding your work, I don't understand from here on : If it's easier to use Maple, how would I do that? Thanks again!

Homework Statement (I translated this from french) Some n dice are thrown and the sum of all their face values is 117. Estimate n through a confidence interval of 90%. In other words, of all the possible rolls of n dice that sum up to 117, find a range in which n should be located 90%...

Thanks a lot for your time, I'll keep you posted on our grade!

Here's the updated image file.

Okay, so I've found the answer to this question but I'd like to know if it's right. Here's what I've got. Check the attachment in my second post (the first one has a small mistake) if you're more of the visual type. Homework Statement What percentage of the area of a square is closer to the...