Π
1
9801
2
2
k=0
∑
∞
(k!)
4
396
4k
(4k)!(1103+26390k)
4
Π
k=0
∑
∞
2k+1
(−1)
k
A
0
=1,B
0
2
1
,T
0
4
1
,P
0
=1
A
N+1
2
a
n
+b
n
,B
N+1
a
n
b
n
,t
n+1
=t
n
−p
n
(a
n
−a
n+1
)
2
,p
n+1
=2p
n
π≈
4t
n+1
(a
n+1
+b
n+1
)
2
π=
k=0
∑
∞
(3k)!(k!)
3
(−640320)
3k
(6k)!(545140134k+13591409)
426880
10005
2
Π
1
2
⋅
3
2
⋅
3
4
⋅
5
4
⋅
5
6
⋅
7
6
⋯
arctanx=
k=0
∑
∞
(−1)
k
2k+1
x
2k+1
π=16arctan
5
1
−4arctan
239
1
π=24arctan
8
1
+8arctan
57
1
+4arctan
239
1
π=48arctan
18
1
+32arctan
57
1
−20arctan
239
1
π=32arctan
10
1
−4arctan
239
1
−16arctan
515
1
π=
−1
ln−1
6
π
2
k=1
∑
∞
k
2
1
π=3+
7+
15+
1+
292+
1+⋯
1
1
1
1
1