Is the sequence $\left(\dfrac 1{n^2 \sin n }\right)$ convergent ? If it does, with what limit?
Asked
Active
Viewed 2,984 times
1
-
1With irrationality measure theory, IIRC the best known bound is $\frac{1}{\sin(n)}=O(n^7)$ – Gabriel Romon Jul 02 '15 at 14:35
-
2See http://math.stackexchange.com/a/20609/148510. Possible duplicate. – RRL Jul 02 '15 at 14:50
1 Answers
-3
If it converges to a not 0 then from 1/n^2->0 and by division we get 1/sinn-->0 or sinn-->infinity which is absurd. If it converges to 0 then 1/(nsinn) -->0 and so n.sinn-->infinity. Thus there is N such that n>N implies that n.sinn is positive. This is absurd too, The sequence does not converge.
Adelafif
- 1,343
-
Your statement beginning with "If it converges to 0" is false, I believe. – Akiva Weinberger Jul 02 '15 at 21:16