用数学归纳法证明:sinx+sin2x+sin3x+……+sinnx=[sin(nx/2)sin((n+1)x/2)]/sin(x/2)
问题描述:
用数学归纳法证明:sinx+sin2x+sin3x+……+sinnx=[sin(nx/2)sin((n+1)x/2)]/sin(x/2)
答
n=1时公式成立;现在假设对n-1公式成立那么sinx+sin2x+sin3x+……+sinnx=sinx+sin2x+sin3x+……+sin(n-1)x+sinnx=[sin((n-1)x/2)sin(nx/2)]/sin(x/2)+sinnx=[sin((n-1)x/2)sin(nx/2)+sinnxsin(x/2)]/sin(x/2)=sin(nx...