Mathematics — Real Analysis · sequences-and-limits
Problem
Let {xn}n=1∞ be a sequence.
a) Show that limn→∞xn=0 (that is, the limit exists and is zero) if and only if limn→∞∣xn∣=0.
b) Find an example such that {∣xn∣}n=1∞ converges and {xn}n=1∞ diverges.