若f(x)=sinπ/2x,则f(1)+f(2)+f(3)+...+f(2012)+f(2013)=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/03 22:06:12
![若f(x)=sinπ/2x,则f(1)+f(2)+f(3)+...+f(2012)+f(2013)=](/uploads/image/z/12675592-64-2.jpg?t=%E8%8B%A5f%28x%29%3Dsin%CF%80%2F2x%2C%E5%88%99f%281%29%2Bf%282%29%2Bf%283%29%2B...%2Bf%282012%29%2Bf%282013%29%3D)
若f(x)=sinπ/2x,则f(1)+f(2)+f(3)+...+f(2012)+f(2013)=
若f(x)=sinπ/2x,则f(1)+f(2)+f(3)+...+f(2012)+f(2013)=
若f(x)=sinπ/2x,则f(1)+f(2)+f(3)+...+f(2012)+f(2013)=
x=偶数时,f(x)=sinπ/2x=0
于是
原式
=f(1)+f(3)+f(5)+...+f(2011)+f(2013)
=sinπ/2+sin3π/2+sin5π/2+……+sin2011π/2+sin2013π/2
=1+(-1)+1+(-1)+……+1+(-1)+(-1)
=0+0+……+0-1
=-1