1)π/4≈1-1/3+1/5-1/7+······+(-1)^(n-1)/(2n-1)
2)π/2≈2 * 2/3 * 4/3 *4/5 * 6/5 * 6/7 *······ * 2n/(2n-1) *2n/(2n+1)
3)π/2≈1+1/3+1/3 * 2/5+1/3 * 2/5 * 3/7+······+An * (n-1)/(2n-1)
import random
import time
def pi_1(n):
pi=0
for i in range(1,n+1):
if i%2==0:
pi=pi-(1/(2*i-1))
else:
pi=pi+(1/(2*i-1))
return 4*pi
# print(pi_1(45))
def pi_2(n):
pi=1
for i in range(1,n+1):
pi=pi*((2*i)/(2*i-1))*((2*i)/(2*i+1))
return 2*pi
# print(pi_2(58))
def pi_3(n):
s=1
L=[1]
for i in range(2,n+1):
s=s*((i-1)/(2*i-1))
L.append(s)
return 2*sum(L)
# print(pi_3(1000))
if __name__=="__main__":
N=int(input("请输入比较整数:"))
t1=time.time()
print(pi_1(N))
t2=time.time()
print("时间大约:",t2-t1)
t1 = time.time()
print(pi_2(N))
t2 = time.time()
print("时间大约:",t2 - t1)
t1 = time.time()
print(pi_3(N))
t2 = time.time()
print("时间大约:",t2 - t1)