Question

若f(x)=sinxπ/6,f(1)+f(2)+f(3)+.+f(102)

Answer 1

f(x)=sinxπ/6

周期=12

所以

f(1)+f(2)+f(3)＋.＋f（12）=0

而

102÷12=8..6

所以

f(1)+f(2)+f(3)+.+f(102)

=f(1)+f(2)+f(3)+.+f(6)

=sinπ/6＋sin2π/6＋.＋sin6π/6

=1/2＋√3/2＋1＋√3/2＋1/2＋0

=√3＋2