Recent content by zebraman

No, but is that important?

Sorry, I don't understand what you're asking.

|s_n - s_(n+1)| = 1/(n+1), so are you saying that will serve as a counter argument? Because doesn't the sequence x_n = 1/n converge?

Well I was thinking the sequence of partial sums of the sequence x_n = 1/n diverges (Harmonic Series). But I guess since |x_n + x_(n+1)|<(1/n) that won't work.

Homework Statement Let (x_n) be a real sequence which satisfies |x_n - x_(n+1)| < (1/n) for all natural numbers n. Does (x_n) necessarily converge? Prove or provide counterexample. Homework Equations Cauchy Criterion for sequences The Attempt at a Solution I figured at first...