Recent content by Demonoid

I understand that the nth harmonic number grows about as fast as the natural logarithm of n, because the sum of ln(n) is integral of 1/x between 1 and n. What I don't understand is what makes ln(n) become the upper/lower bound of the nth harmonic number ? What makes it bigger or smaller, so it...

Homework Statement Ok, basically I need to show that Ʃ 1/n (between 1 and n) (which is harmonic number) is θ (big theta) of ln(n), which means that is it bounded below and above by this function(upper and lower bound). But I don't quite understand how to prove it.Homework Equations I know...

Basically I need to find a mistake in this "proof". I claim that 0,1,2,3...are all even. I will use induction to prove that 'n is even' for n = 0,1,2,3... Base case is n = 0, which is true, 0 is even. I assume that the statement is true for n = 0,1,2,3...,k and consider n = k+1. By...

a little bit more explanation with sample solution will be helpful. What you said doesn't help a bit. I know that it is an arithmetic formula (4n-1). The sum on the other hand is not.

I'm a little stuck here... I need to write this in the summation notation, and then find and prove a formula in terms of n, using induction :3+7+11+...+(4n-1) I know that the summation notation is n +--- \ / 4i-1 +--- i=1 but I have no idea how to...

I'm a little stuck with these bad boys: Let P(x) be the assertion “x is odd”, and let Q(x) be the assertion “x is twice an integer.” Determine whether the following statements are true: 1. (Vx ∈ Z)(P(x) ⇒ Q(x)) 2. (Vx ∈ Z)(P(x)) ⇒ (Vx ∈ Z)(Q(x)) My attempt: I don't get the statement at all...

URGENT Field Proofs help. I need to prove the following: 1) Prove that if x, y are elements of a field, and X x
Y = 0 then either x = 0 or y = 0 . Write a detailed solution. and mention which of the eld axioms you are using. 2) Let F be a field in which 1 + 1 = 0 . Prove that for any...

I've given a function where f: R->R, and need to determine an image(or range): f(x) = x/(1+|x|) I've pretty sure the image is R, but I'm not positive: Heres my attempt: y/1 = x/(1+|x|) y(1+|x|) = x y+ y|x| = x y|x| = x - y... I'm kinda stuck here, since I can't determine an image...

I need to graph/find numbers for S∩T where S is x^2+y^2 <=100 and T is x+y<=14. I know I can find them simply by choosing/picking them, but are there any other solution ? I thought maybe doing x^2+y^2 <=100 + x+y<=14 = x^2+y^2 + x+y<=14 +100 = x^2+y^2 + x+y<=114 = x^2+y^2 <=...

(x-z)^2 - 4yx - 4yz +4y^2 + 8y >= 0 is this right ?

Ok, I think I'm getting closer: Here's what I've got: (x-z)^2 - 4(yx - yz + y^2 + 2y) >=0 now I get why y = 0, would give me (x-z)^2... but how would y be equal to 0 ?

I don't get this clue :-p How's y ever going to be 0 ? Even if y is 0, it will be (x+z)^2 >= 4xz, which isn't very helpful... I need to prove this: (x-2y+z)^2 >= 4xz -8y. using this: x+z<=2:I can't seem to simplify (x-2y+z)^2 >= 4xz -8y enough to get x,y,z by themselves.. I expanded first...

Question: I need to prove this inequality: Where x,y,x are non-negative and x+z<=2: (x-2y+z)^2 >= 4xz -8y. My attempt: I thought maybe choosing x as 0 and z as 0 will and then solving for y... but that only yields y+2 >= 0, which isn't really a solution, since I can't choose numbers...