因为arctanx(x)=x-1/3*x^3+1/5*x^5-1/7*x^7+1/9*x^9...
上式中令x=1有
π/4=1/1-1/3+1/5-1/7+1/9-1/11+1/13-1/15+.
两边同乘以4即得结论.