Recent content by cnwilson2010

I neglected to put the condition that bn is also monotone. So I was thinking of an with a different sign than bn but this doesn't seem to change much either.

Homework Statement Let an be monotone sequences. Prove or give a counterexample: The sequence cn given by cn=k*an is monotone for any Real number k. The sequence (cn) given by cn=(an/bn) is monotone. Homework Equations The Attempt at a Solution On the first one, I don't...

Didn't want to be oddly transcendental or anything, so I was trying to stay away from those, but found out later they would have been fine. So thank you for that.

Thank you. How about 1/n(2(1/2))?

Hi. I found some rational sequences that converge to irrational limits, but am not having any luck going the other direction, i.e., an irrational sequence that converges to a rational limit. Any suggestions?

Homework Statement n2<=2n n is a natural number For what values of n is the statement true and prove by induction. Homework Equations The Attempt at a Solution I tried 1 and it worked, I tried 2 and it worked, just for fun I tried 3 and it didn't work, so I assumed the...

Thank you for your replies they were very helpful. Now I'm working on n2<=2n. For what values of Natural numbers is this statement true and prove by induction. Obviously, 1 and 2 are true, now I'm thinking proof by contradiction and the idea of the existence of a least member of the set. Does...

Homework Statement Prove: 1^3 + 2^3 +...+n^3=(1+2+...+n)^2 n=Natural number Homework Equations The Attempt at a Solution Using induction - n=1 obvious Assume for n=k equation is true. Show for k+1. I have that the right side prior to k+1 is (k^2(k+1)^2)/4 After k+1 I...