Question

已知函数f(n)=sin(nπ)／6,(n∈Z).求值f（1）+f(2)+f(3)+……+f(102) 额……我想问的不

Answer 1

sinπ/6+sinπ/3和sin2π/3+sin5π/6不是互为相反数的

sinπ/6= sin5π/6=1/2, sinπ/3=sin2π/3=√3/2

f(n)=sin(nπ)/6的周期T=2π/(π/6)=12

n需从1取到12为一个周期,

一个周期f(1)+f(2)+.+f(12)=0

∴f（1）+f(2)+f(3)+……+f(102)

=f(1)+f(2)+f(3)+f(4)+f(5)+f(6)

=sinπ/6+sinπ/3+sinπ/2+sin2π/3+sin5π/6

=1/2+√3/2+1+√3/2+1/2=2+√3