answersLogoWhite

0

No. The sequence (n*sin(n)) is not properly divergent. To be properly divergent it must either "tend to" +inf or -inf. We say that (xn) tends to +inf if for every real number a there exists a natural number N such that if n>=N, then xn>a.

It is clear that no such N exists for all real numbers because n*sin(n) oscillates (because of the sin(n)). Therefore (n*sin(n)) is not properly divergent. This is not a rigorous proof but the definition of proper divergence is precise and can be used for any proof dealing with proper divergence.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
BlakeBlake
As your older brother, I've been where you are—maybe not exactly, but close enough.
Chat with Blake
RafaRafa
There's no fun in playing it safe. Why not try something a little unhinged?
Chat with Rafa

Add your answer:

Earn +20 pts
Q: Is nsinn properly divergent
Write your answer...
Submit
Still have questions?
magnify glass
imp