Question

show that this sequence diverges

Answer 1

\[\huge \sum_{k=3}^\infty k \sin (\frac{ 1 }{ k })\]

Answer 2

by limit test, you can prove this
http://www.wolframalpha.com/input/?i=summation+k%3D3+to+infinty+%2C+k+sin%281%2Fk%29

Answer 3

yeah i already checked that but i need the proof,thank

Answer 4

well am not too sure if my method is right, i have never studied about proving whether a series is convergent or divergent ,
if we represent this series as f(k),
at k-> inf, f(k) =1 , since f(k) is not 0 at k-> inf, can we conclude this series is not convergent ?