I would like to know why \(\displaystyle{\frac{{{\sin{{\left({n}\right)}}}}}{{{n}^{{2}}}}}{

fanairana7lu1

fanairana7lu1

Answered question

2022-04-07

I would like to know why sin(n)n2<1n2? It becomes obvious when you look at a graph, but for instances where you can’t do that how do you tell if the comparison is true?

Answer & Explanation

anita1415snck

anita1415snck

Beginner2022-04-08Added 19 answers

We have that sin(x)=1 if and only if x is π2+2kπ for some integer k.
π2+2kπRQ,
hence sin(n)1 for all nN. As |sin(x)|1 you find out that sin(n)<1, therefore your strict inequality.
Vegljamzt6

Vegljamzt6

Beginner2022-04-09Added 16 answers

nN
n  can't be  kπ2
nNkπ2Qc
1sin(n)1  turn into  
1<sin(n)<1
so
sin(n)n2<1n2

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