已知f(n)=sin(npai/4),则f(1)+f(2)+…+f(2012)等于多少?

Question

已知f(n)=sin(npai/4),则f(1)+f(2)+…+f(2012)等于多少?

Answer 1

由题意可知f{1}+f{2}+f{3}+f{4}+f{5}+f{6}=0
所以原式=(f{1}+f{2}+f{3}+f{4}+f{5}+f{6})~+f{2006}+f{2007}+f{2008}+f{2009}+f{2010}+f{2011}+2012}
=f{2011}+f{2012}
=f{1}+f{2}
=sinπ/3+sin2π/3
=√3