Power series- sine series

#sine series
from pylab import*
def fact(n):
    if n<=1:
        return(1)
    else:
        return(n*fact(n-1))
x=linspace(0.0,8*pi,100)
y=sin(x)
sinp=[]

for k in x:
    sum=0
    for i in range(0,31):
        sum+=(-1)**i*k**(2*i+1)/fact(2*i+1)
    sinp.append(sum)
   
plot(x,y,x,sinp)
show()