You can use the comparison test. Since the convergent sequence divided by n is less that the convergent sequence, it must converge.
Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.
(0,1,0,1,...)
no converse is not true
It could be divergent eg 1+1+1+1+... Or, it could be oscillating eg 1-1+1-1+ ... So there is no definition for a sequence that is not convergent except non-convergent.
The closing of the mitral and tricuspid valves produces the S1 sound, followed by the closing of the aortic and pulmonic valves, which produce the S2 sound. In sequence, it sounds like "lub-DUB, lub-DUB, lub-DUB".
If a monotone sequence An is convergent, then a limit exists for it. On the other hand, if the sequence is divergent, then a limit does not exist.
A convergent sequence is an infinite sequence whose terms move ever closer to a finite limit. For any specified allowable margin of error (the absolute difference between each term and the finite limit) a term can be found, after which all succeeding terms in the sequence remain within that margin of error.
i believe it is lub lub (loob loob) as in tib ya lub lub (i love you)
lub tub lub tub lub tub....
Lexicographic preferences are not continuous because of the decreasing convergent sequence.
Break down phrases into word meanings. Predominant means primary (at this moment). Rhythm is a noticeable timed or untimed sequence of events-- for example, a song has 3 short beats followed by 6 rapid beats; that is that song's rhythm. Atrial Fibrillation (or A-Fib) is a sustained rapid "quivering" of the heart, rather than normal systole. A-Fib does not let the heart chambers, especially the ventricles, rest. A normal heart would be lub-lub, pause, lub-lub, etc. But A-fib is more like lub-lu-lub-lu-lub-lu... rapid and continuous. A-Fib is a medical emergency that needs corrected before the underlying problem causes the heart to stop.