2(sinx/2)*∑sinkx=(cosx/2)－cos(2n＋1)*x/2这怎么证明

用积化和差公式2sin(a)sin(b)=cos(a-b)-cos(a+b)则2sin(x/2)*sin(x)=cos(x/2)-cos(3x/2)2sin(x/2)*sin(2x)=cos(3x/2)-cos(5x/2)2sin(x/2)*sin(3x)=cos(5x/2)-cos(7x/2)。。。2sin(x/2)*sin(nx)=cos((n-1/2)x)-cos((2n+1)x/2)上面所有式子相加得到左边=2(sinx/2)*∑sinkx=右边=(cosx/2)－cos(2n＋1)*x/2)