# interesting

1. ### Very Interesting Sum. Need Help !

Hello, today I need help whith sums that should require calculus methods. Here is the problem : Prove that : So we can easily see that : Using this same method, we get to : But from there I am blocked :(. I really need help !
2. ### Interesting problem involving inverses.

This is a problem that came about by my own mathematical meanderings: g is the inverse of f, so: f(g(x)) = x g(f(x)) = x f'(x) = g(x), solve for f(x). I've derived the formula d/dx g(x) = 1/f'(g(x)) to save a bit of work. I'm not sure if such a function exists, and even if it does, whether...
3. ### Looking for help on a sequence question - interesting problem

Hi Everyone, I hope this is the right place for a sequence question but I'm stuck. I can solve it programatically but not mathematically and think I'm missing something. A series is formed with an original value of 2 and each following term in the sequence given by the previous term + the...
4. ### Interesting Question

I just noticed this question in another forum and was puzzling around a bit with this one to find a solution. If A= [k3 + (k+2)3+(K+4)3+(K+6)3+...........(k+38)3 ] and B=[k+(k+2)+(k+4)+(k+6)+.........(k+38)] ,then what is the remainder if A is divided by B (for every positive integer k).
5. ### Interesting problem

Hi everybody Please provide the solution and answer on the following problem On which of the two days of the week, Saturday or Sunday, does New Year's Day fall more often? thanks in advance .
6. ### Interesting Interest

Suppose one borrowed $400.00 per month for 54 months at 6 percent. After final$400.00 one waited 3 months and began repayment of loan at $200.00 per month for 72 months, then increased to$600.00 per month until loan was paid off. 1) what would be amount of interest owed before repayment...

This is a good write-up on Stephen Wolfram.
8. ### An interesting algorithm

For natural number N,we can take the smallest and largest prime divisors and get the sum of them and repeat the process as many times as we want.For example N=3 => sum of the smallest and largest prime divisors is 3+3=6 => 2+3=5 => 5+5=10 => 2+5=7 etc... Prove that we can get a square number by...
9. ### Interesting question

Suppose 150 people joined 3 different communities in Google+. The communities are for 1. Mathematics, 2. Hot Peppers and 3. Cooking Here is what is known: 1. 90 joined Mathematics community 2. 50 joined Hot Peppers community 3. 70 joined Cooking community 4. 15 joined Mathematics and...
10. ### Interesting result of lim k—»0

I discovered this interesting result while working on another problem. \lim_{k \to 0}\frac{e^{kx}-kx-1}{e^k-k-1}=\ ? Can you solve it? I have the answer; please PM me if you'd like to see it. I'll post it here in a few days. Good luck! Cheers, ~ Justin
11. ### Interesting math/programming problem....

The problem is simple, let me describe it: Suppose i ask 5 questions to 3 students and they give their answers. Every student is able to see what every student had answered. All the questions have a YES/NO answer. The correct answers are not given be me to the students, but i give to all...
12. ### Interesting limit problem

We need to show the following, Lim X-> 1 [X(X-1)T+1]^(1/(1-X)) = EXP(-T) Obviously we need to apply L'Hopitals rule, but it is not straight forward how to proceed !
13. ### Exponents Interesting Dilemma -

Hi Everyone, Kind of new around here, but maybe someone can take a look at this and offer some advice. I'm struggling with some exponents, anyone care to help? -(-c4)-4) = 1/c16 however Maple 17 returns a different result -(-c4)-4) = -1/c16 I have attached a PDF of a Maple page if anyone is...

15. ### interesting circle problem

I found this the other day online, and its fairly interesting: a circle is inscribed in a 36 degree sector of a circle with an area of 25(pi) cm squared. What is the circumfrance and area of the smaller circle? I'm having some trouble wrapping my head around it though. any help?
16. ### Interesting question regarding the solution to a trigonometric equation

I just saw a very simple question that has generated a lot of interesting discussion within our department. Our trigonometry teacher put the question on the board: Solve: tan(x) = 1/csc(x) Naturally, all the students (and the teacher as well), applied the identity 1/csc(x) = sin(x) and...
17. ### Interesting stock question

How would you calculate the economic order quantity given that there is no holding stock?
18. ### Proof of interesting equation: Related Topics, groups, semigroups, binary operations

Here is the question: "Let G= Z x Q (Where Z is the set of integers and Q is the set of rational numbers) and define a binary operation o by (a,b) o (c,d) = (a+c,2-cb+d) - (*) Is (G,o) (i) a semigroup, (ii) a group? You must give full reasoning for...
19. ### An Interesting Integral

Prove that \int_0^1 \ln \left( \Gamma(1+x)\right)dx = \frac{1}{2}\ln(2\pi)-1
20. ### interesting problem with a function (not defined) - quite intimidating

I found this question to be quite intimidating: Suppose a function f has the following properties: f is differentiable everywhere. For all values of x and y, . . . a) Show that: b) Show that for all values of x by first showing that for all x. c) Use the definition of the derivative to...