Question

若f(x)=sin(π/6)x,则f(1)+f(3)+f(5)+~~~~ +f(2011)

Answer 1

f(1)+f(7)

=sin(π/6)+sin(7π/6)

=sin(π/6)+sin(π/6+π)

=sin(π/6)-sin(π/6)

=0

同理

f(3)+f(9)=0

f(5)+f(11)=0

也就是说,每6个数之和为0

原式,从1到2011,共有(2011-1)/2+1=1006个数

1006/6=167.4

原式=f(1)+f(3)+f(5)+f(7)

=f(3)+f(5)

=sin(3π/6)+sin(5π/6)

=1+1/2

=3/2