收敛解析：∵ sinx≤x(x>0)∴ sin(π/2^n)≤π/2^n∵ 公比q=1/2∴ ∑(π/2^n)收敛∴ ∑sin(π/2^n)收敛PS：f(x)=sinx-x(x≥0)f'(x)=(sinx-x)'=cosx-1≤0∴ f(x)单调递减∴ f(x)≤f(0)=0∴ sinx-x≤0∴ sinx≤x
