Recent content by scooterboot1

since i can show that c^n*x0>xn and since c^n -> 0 then I can use the squeeze theorem to show that {xn} goes to zero... just want to make sure I made sense of that correctly

I understand why lim n -> ∞ c^n = 0, but I don't understand how it relates to the problem. I need to determine why {xn} goes to zero

Homework Statement Suppose {xn} is a sequence of positive numbers for which there exists c, 0<c<1, such that ([x][/n+1])/([x][/n])<c for all n in Z+. Prove that [x][/n] goes to zero. Homework Equations The Attempt at a Solution Let the first term of {xn} be x, where n=1. Then by...

sorry, I miswrote the question, it was "what are the subsequences of {xn}", I think it refers to subsequences that you can define like I did previously using n

Homework Statement What are all of the subsequences of {xn}? Homework Equations {xn}={1, 1+1/2, 2, 1-1/2, 1, 1+1/3, 3, 1-1/3, 1, 1+1/4, 4, 1-1/4, 1, ...} The Attempt at a Solution So far I have: {1}, {1+1/n}, {1-1/n} and {n} but I can't find any more... I am pretty sure there are...