# strange

1. ### strange integral

So I've stumbled upon to an indefinite integral (sqrt(1+x^4))/(1-x^4) don't know where to start. I've tried multiplying/dividing with sqrt(1+x^4) but no use.
2. ### convergence of a strange (but probably easy) series

I have the series: summation from 1 to infinity (-1)^n*n^5. It seems easy but I can't find the correct test. It looks like it diverges, but I'm not convinced. Please help! Bret
3. ### This is really strange

We know that a^m * a^n = a^(m+n) But s^(1/2) * s^2 is not equal to s^[(1/2)+2] This doesn't make any sense Either this is an unspecified* exception to this rule, OR this formula is not a mathematical rule at all *unspecified in context to mine and several other text books
4. ### A strange way to write 0

Let $K \leq 3$ an integer. Prove that $$\underset{i=0}{\overset{K}{\sum}}\frac{\left(-1\right)^{i}}{i!}\frac{\left(K-i-1\right)^{2}}{\left(K-i\right)!}=0.$$
5. ### Strange probability problem

Hi I am facing a probability problem....cant seem to understand how this is structured Problem: ROW 1 - Every month a set of new customers come and join a website. The first row (pasted below) clearly show how with a sample data. These customers are new as in they are registering for the...
6. ### Word Problem involving strange rules for number sets and permutations...def beyond me

Trying to work out the amount of permutations in a number set that behaves in this manner: "This is a reincarnation problem. There are six incarnations of artists. Three are alive and three are waiting in limbo to be reborn. There is always a Child, an Apprentice, and a Old Master. As the Old...
7. ### Strange notation for continuity

I just ran across a problem that has the following notation: C_{0}^2[0, 1]. I already now what C^2[0, 1] means. But what the heck is that subscript zero??
8. ### Proving a metric space with a particularly strange distance is bounded and separable.

Hi everyone! I'm trying to solve a problem related to metric spaces and I'm having a really hard time. Here's the given statement: Let (A,d) be a metric space of sequences defined as follows: 1) Any sequence in A is a sequence of natural numbers 2) For all (a_n)_n, a_n<a_(n+1) (strictly...
9. ### Strange problem with chain rule

derive x/(1-x^2) - Wolfram|Alpha How on earth does 1-x^2 become x^2-1?! Thanks.
10. ### Strange diophantine equation

k,a,b,c,d be positive integers Solve the system of equations 3^k-2=abcd 2(3^{k-1}-1)=(a-1)(b-1)(c-1)(d-1) or prove that no solutions exist
11. ### integration strange function

Hi, I am unsuccessfully straggling to integrate the following Please, can somebody explain to me how to solve it. Thanks.
12. ### Limit of a strange sequence

Define sequence by a_0 = 1 and a_(n + 1) = cos(a_(n)/2). Given that |cos(x) - cos(y)| < (or equal to) |x - y| use this to show that cos(a_n/2) -> cos(a/2). Not exactly sure how to get this. I'm probably being inane here. This question comes under Cauchy sequences..
13. ### Strange Prob. Problem

Hello! I am not sure whether I should place this in the advanced or normal statistics sections. This is because I am not actually asking for this information for a class, but would like to know for my own use. How could I solve problems like this word problem: "A bag contains black and...
14. ### Strange factorials

\\ 10 \cdot 9 \cdot 8 \cdot 7 = 7! \\ \\ 6 \cdot 5 \cdot 4 = 5! \\ \\ \text{Does anybody know or can generate other cases like this? Where you have a product of consecutive integers, not including 2,} \\ \text{and this product is equal to the factorial of one of the integers used in the...
15. ### I'm struggling to solve this strange simultaneous equation. Can someone help me?

Solve the pair of simultaneous equations: x+y=2xy x-y=xy I solved it to get x=2 and y=0.66 but the answer booklet says it is wrong? can someone please explain
16. ### Solve the following...I keep getting strange answers

x + \frac{7-2x}{x-2}<= \frac{5x+7}{x-2} Solve and express solution as a graph and in interval or set notation. The solutions are x=0 or x=9. (That's given.) My work: he factors I find are x and x-9. Test the factors in the intervals...if their product is - then that interval works...
17. ### A strange property of the Quadratic ecuation

I´ve found a strange and difficult to prove formula that derived from two quadratic equations. "If two quadratic equations:Ax^2+Bx+C=0 and Dx^2+Ex+F=0 share one solution. then: (CD-FA)^2=(BF-EC)(AE-BD).......(1) is always true." If they are equivalent, It is known that their coefficients are...
18. ### Strange Confidence Interval question.

Stats exam is less than a week away and while looking through a past paper I found a question that seems very poorly written. "Given that u = 1000, state the probability that a 98% confidence interval for u will not contain 1000." (I put u for the Greek Mu (mean)) How can a confidence interval...
19. ### Strange Integral Question (possbily parametric)

Find \frac{d}{dx}\ \int \frac{sin(t^3)x}{t^2}dt - the upper boundary for the integral is 4+x^4 and the lower is 2+cos^2(x) I wouldn't even know what to search for to learn about this type of integral...
20. ### Riemann Summ Limit Proof (strange question to me)

Recall the definition of teh Riemann Sum S(f;\pi ;\xi) for a function f:[0,1]\rightarrow \mathbb{R}. Let f:[0,1]\rightarrow \mathbb{R},\ x\rightarrow \frac{5}{6}x[/latex] For the partition \pi_n of [0,1], 0=t_0<t_1<...<t_n,\ t_j\ =\ \frac{5}{n},\ j=0,...,n and \xi_j =\ \frac{2}{3}t_j\ +\...