Recent content by glomar

Probably it was an error from the Professor. I'll check that. Thanks!

Homework Statement I have to solve the following integral 1/(sqrt[x] * ln[x]) from 2 to infinity Homework Equations The Attempt at a Solution u= ln[x] dv=1/sqrt(x) du= 1/x v= 2 sqrt(x) If I do this I get lim (ln b/ sqrt[x] - 4 sqrt[x] -...

Thank you for the typing suggestions. I'm still trying to put the subscripts. Here is my proof about xn * xn+1 >= 2 for all n >= 1. For n=1 , x1 * x2 = 2 so it's true. Suppose that xn * xn+1 >= 2 is true. Then, xn+2 * xn+1 = (1 + 1/xn) xn+1 = xn+1 + 1 = (1 + 1/xn) + 1 = 1/xn + 2...

Yes, So far what I have is abs((x(n+2)-x(n+1))= abs(1/x(n) - 1/x(n+1)). I think what I have to prove by induction is x(n)>=1. So, for n=1 , x1=1 is true. Assuming n=k and x(k) is true, I have that x(k+1)= 1+ 1/x(k). Since x(k)>= 1, 1/x(k) < 1. So 1+ 1/x(k) >=1. I'm I in the right...

Homework Statement Consider the sequence (x(n)) defined recursively by x(1)=1 and x(n+1)=1+1/x(n). Prove that abs[x(n+2)-x(n+1)]<= 1/2 abs[x(n+1)-x(n)]. Homework Equations The Attempt at a Solution Proof by induction. For n=1, abs(x(3)-x(2))<= 1/2 abs(x(2)-x(1))...