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You mean the way i proved $$\lim_{n\rightarrow +\infty}\frac{n}{1 + n(a_n)} = \infty$$H How about this: $$\lim_{n\rightarrow +\infty}\frac{n}{1 + n(a_n)} = \lim_{n\rightarrow +\infty} n * \lim_{n\rightarrow +\infty} \frac{1}{1 + n(a_n)}=\infty*1=\infty$$. I have $$\lim_{n\rightarrow...

Homework Statement Let $$(a_n)$$ be a sequence such that $$\lim_{n\rightarrow +\infty}n(a_n)=0$$. 1) What is $$\lim_{n\rightarrow +\infty}(1 + {\frac{1}{n}} + (a_n))^n$$ 2) For which value of p and l, after some n is $$(b_n)=\frac{n^{p \ cos(n\pi)}}{(1 + l + (a_n))^n}$$ properly defined. p...

I don't think that motivation will make you work around the clock, work ethic will. I once heard someone along the lines: Motivation gets the ball rolling, work ethic/discipline keeps the ball rolling. That being said i think best way to develop work ethic is to develop work habits. Since you...

Homework Statement Let f: R -> R and defined with f(x)={ x, if x \in Q or x^2 if \in R\Q} a) Prove that function is discontinuous at x=2; b) Find all points for R in which function is continuous; The Attempt at a Solution As far as i know there are infinitely many irrationals but more...

Since you gave counter example you assumed that S is an order set with least-upper-bound property. (Right?) If so then this means that if E is subest of S, and E is non empty and E is bounded above , then sup E exists in S. So let S = (0,1) ##\cup## (2,3) and Let E= (2,3). E is subset of S...

If i may usk where does least-upper-bound property come into play in your counter example?

Theorem: Suppose S is an ordered set with the least-upper-bound property, B⊂S, B is not empty, and B is bounded below. Let L be the set of all lower bounds of B. Then α=supL exists in S, and α=infB. Rudin proves that α=supL, α is an element of L and that α=infB. For α to be sup i.e. lub it...

Good points, there goes my proof in the water.:cry:

Homework Statement If p is a prime and k is an integer for which 0<k<p, then p divides \displaystyle \ \binom{p}{k}. Whne p divides \displaystyle \ \binom{p}{k} it means that \displaystyle \ \binom{p}{k}=p*b. wheren b is some number. The Attempt at a Solution So p is equal to some number k...

Fall Semester: 1. Analysis 1A 2. Linear Algebra A 3. Programming 1 4. Introduction to Mathematical Logic 5. English 1

I apologize if somebody had already posted this.

The question was: How many real number solutions are there for 2^x=-x^2-2x. I tired for an hour to isolate x but i couldn't do it. Then i used wolfram alpha and it gave me two solutions and graph. I realized that question was, how many not what are the solutions, and i could do that by graphing...

Homework Statement Numbers a,b,c are consecutive members of increasing arithmetic progression, and numbers a,b,c+1 are consecutive members of geometric progression. If a+b+c=18 then a^2 +b^2 + c^2=?The Attempt at a Solution a + b + c= 18 a + a +d +a + 2d = 18 3a + 3d = 18 3(a+d)= 18 a+d=6=b...

As i have understood it there exist separate arithmetic and separate geometric progression. This is a first time i hear of arithemtico-geometric series.

Wel its evident that two solutions are 1 and - 1 but what kind of geometric progression is with r=1 or r=-1?