已知f(n)=sin nπ/6,求证f（n+12）=f(n)

题目

已知f(n)=sin nπ/6,求证f（n+12）=f(n)

答案

f(n+12)=sin[(n+12)π/6]
=sin(nπ/6+2π)
=sin(nπ/6)=f(n)
命题得证