Recent content by grief

What are you thoughts on numbers 2 and 3? For number 2, note that the domain of f(x) is the set of all points but 0, since you're not allowed to divide by 0. The domain of g(x) is all x>=-1 (or else you'd be taking the square root of a negative number, which is not allowed, either). How do...

Just to clarify, the method I'm proposing is NOT treating the sum as an integral. Rather, it's to integrate the expression to yield an easier expression which you can evaluate. Then you would need to take the derivative of that to get back the desired result. I'll show you a different method as...

Try to evaluate the sum of (i+1)a^i from i=1 to n first. Integrating (i+1)a^i with respect to i, you get a^(i+1). Now, you have n terms in the sum. The integral of the sum is simply the sum of the integrals of the individual terms, i.e. the sum of the terms a^(i+1) from i=1 to n. This you...

*EDIT* I'm sorry, I realize a different version of the problem is easier to do with calculus. That's the sum of (i+1)a^i.

It seems to me that there is no order of convergence in this case, according to the definition you gave. Try to plug the formula into the definition of order of convergence. \frac{5}{6}^{{(n+1)}^2} / {(\frac{5}{6}^{n^2})}^p = \frac{5}{6}^{{(n+1)}^2-pn^2}. If p<=1, then the exponent tends to...

There are different ways of doing this. There is a way to do it using calculus. Think about letting a be a variable, and integrating to get another expression that you know how to evaluate.

There are different ways to think of what vectors and vector spaces are. One way in which vectors are introduced in high school is "arrows" that have a magnitude and a direction. These arrows may be in R^n for any n. An arrow is a nice way of visualizing it, but really vectors may simply be...

Thanks for the reply! Though I'm still having trouble with the universality part. I need to decide two things: the morphism of abelian groups from M to \mathcal{T}(M), and, given a morphism f of abelian groups from M to a ring R, a morphism of rings from \mathcal{T}(M) to R making the...

i)What do you know about the sum of independent Poisson variables? (Hint: It's also Poisson). ii)Let Z=X+Y. How do you find E(Z^2) in terms of the mean and variance of Z, which you should know?

It seems from the problem statement that you are required to be correct, not just have a good guess. That seems to be impossible, though I do remember a variant of this problem which was possible: "one box has two black marbles, one with two white marbles, and one with one of each. The boxes...

If you think about it, a change of +-1 doesn't much matter. Suppose I guess 1006, and am told "too high." In the traditional game, I would conclude the number I have to guess next lies between 1 and 1005. Now I would conclude the number I have to guess next lies between 1 and 1006. So I would...

Think about what each of the definitions mean. It seems that it's a pretty strong condition that a path touching each vertex once also covers each edge once. Specifically, it means the graph needs to have only the edges in the hamiltonian cycle, and no others. See if you can go from here to find...

I'm reading a book on category theory and I'm stuck on this problem: For a given abelian group, what is the universal morphism to the forgetful functor Ring->Ab taking each ring to its underlying additive group? I think if the functor was Ring -> Monoid taking each ring to the underlying...

Can you clarify what exactly your question is? Are you trying to prove "min{an/bn}<=sum(an)/sum(bn)<=max{an/bn}"? If this is what you're trying to prove, where do you get stuck?

CharmedQuark, what you said isn't exactly correct, since your constructed function from N to AxB won't be surjective.