ThatGuy

Let s(n) = ((a^n)+(b^n))^(1/n), where 0<=a<=b. Prove that s(n+1) <= s(n). In other words, prove that the sequence {s(n)} monotonically decreases.

In three dimensions, what does |x(3)| <= 1 - x(1)^2 - x(3)^2 look like?

In the past week I've developed both a severe cold and I guess what one might call mild insomnia (for the past three nights, despite much effort, I have only been able to log approximately 2-3 hours of sleep).

As weightlifter, I realize that these are both symptoms of overtraining. However, I am reluctant to concede without some further advise that I am experiencing overtraining syndrome considering 1) I have not been experiencing abnormal muscle soreness, and 2) have made some pretty solid gains on my bench and other exercises during this past week.

Now, I'm wondering if it could possible by 1) The protein shake I ingest before bed acting as an accelerant (just like caffeine) that's keeping me awake, or 2) my debilitated breathing from my cold is disturbing my sleep.

Any thoughts are much appreciated.

A chord is drawn between every two points on the perimeter of a circle. There are n points on the perimeter. Every two chords intersect at a point either on the perimeter or inside the circle.

a) Determine the number of chords drawn.

b) What is the number of intersection points on the perimeter?

c) What is the maximum number of intersection points inside the circle?

d)What is the maximum number of chords which can go through any single intersection point inside the circle.

Let d be a positive integer. Shoe that there must exist an integer of the form 111...100...0 - that is one which consists of a sequence of ones followed by a sequence of zeroes - which is divisible by d.

a and n are both natural numbers. a is prime.

Let n be a positive integer. My professor’s definition of a binary representation of n is a set of integers c{0}, c{1}, …,c{r} with c{r}=1 and c{i} € {0,1} for 0<= i < r satisfying:

n=c{r}2^(r)+c{r-1}2^(r-1)+…+c{1}2^(1)+c{0}

Brackets indicate subscripts

Please help me with the FORMAL proof. Much thanks in advance.

I need help with Linear Algebra Proofs!

After some work I believe the answer is no, but I'm asking this question to check my work and see if I missed something. Thanks for any help in advance.

This is for a quantitative econ class. I'm not too familiar with metric spaces, so I could use some help. Thanks in advance!

d(x,y)=1 if x does not equal y

d(x,y)=0 if x = y

Linear Algebra proof! Much help needed!

Let V be a finite deimensional R-vector space.

Let V* = {$: V --> R, $ linear}.