let be x \in R I want to show that if \lim_{n

urlacainnxp

urlacainnxp

Answered question

2022-01-22

let be xR
I want to show that if
limnsin(nx)=0
then
sin(x)=0

Answer & Explanation

Eleanor Shaffer

Eleanor Shaffer

Beginner2022-01-23Added 16 answers

sin(n+1)x=sin(nx)cosx+cos(nx)sinx. So sin(nx)0 implies that cos(nx)sinx0. If sinx0 this gives cos(nx)0. But then 1=sin2(nx)+cos2(nx)0 , a contradiction.

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