tangent
Not Supported
x
-
1
-
1
2
-
1
4
-
1
5
-
1
6
-
1
9
-
⋯
=
1
Search
Returned 97 matches (100 formulae, 55 docs)
Lookup 16.844 ms, Re-ranking 1901.111 ms
Found 222920 tuple postings, 88494 formulae, 15993 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
2.3775
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
x
-
1
-
1
2
-
1
4
-
1
5
-
1
6
-
1
9
-
⋯
=
1
x
-
1
=
1
+
1
2
+
1
4
+
1
5
+
1
6
+
1
9
+
⋯
x
-
1
-
1
2
=
1
+
1
5
+
1
6
+
1
7
+
1
10
+
1
11
+
1
12
+
⋯
1
2
=
1
3
+
1
9
+
1
27
+
1
81
+
⋯
x
=
1
+
1
2
+
1
3
+
1
4
+
1
5
+
1
6
+
1
7
+
1
8
⋯
1
=
1
2
+
1
4
+
1
8
+
1
16
+
⋯
x
-
1
=
1
+
1
3
+
1
5
+
1
6
+
1
7
+
1
9
+
1
10
+
1
11
+
⋯
Doc 2
0.4034
3.3651
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
∑
n
=
1
∞
1
n
(
2
n
n
)
=
1
-
1
2
+
1
4
-
1
5
+
1
7
-
1
8
+
⋯
3
3
4
(
1
-
1
2
2
+
1
4
2
-
1
5
2
+
1
7
2
-
1
8
2
+
1
10
2
±
⋯
)
π
4
=
∑
n
=
0
∞
(
-
1
)
n
2
n
+
1
=
1
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
∑
k
=
1
∞
(
-
1
)
k
s
k
-
1
=
1
1
-
1
2
+
1
6
-
1
42
+
1
1806
±
⋯
∑
n
=
0
∞
(
-
1
)
n
n
!
=
1
0
!
-
1
1
!
+
1
2
!
-
1
3
!
+
1
4
!
-
1
5
!
+
⋯
∑
n
=
1
∞
(
-
1
)
n
+
1
n
!
=
1
1
!
-
1
2
!
+
1
3
!
-
1
4
!
+
1
5
!
-
1
6
!
+
⋯
∑
n
=
1
∞
(
-
1
)
⌊
n
-
1
2
⌋
2
n
+
1
=
1
1
+
1
3
-
1
5
-
1
7
+
1
9
+
1
11
-
⋯
π
2
12
=
∑
n
=
1
∞
(
-
1
)
n
+
1
n
2
=
1
1
2
-
1
2
2
+
1
3
2
-
1
4
2
+
1
5
2
-
⋯
∑
n
=
1
∞
1
n
2
n
=
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
1
1
-
1
2
+
1
3
-
1
4
+
⋯
π
3
32
=
∑
n
=
1
∞
-
1
n
+
1
(
-
1
+
2
n
)
3
=
1
1
3
-
1
3
3
+
1
5
3
-
1
7
3
+
⋯
∑
n
=
0
∞
(
-
1
)
n
x
2
n
+
1
2
n
+
1
=
1
2
-
1
3
⋅
2
3
+
1
5
⋅
2
5
-
1
7
⋅
2
7
+
⋯
For
x
=
1
/
2
=
1
π
(
1
2
-
1
3
⋅
2
3
+
1
5
⋅
2
5
-
1
7
⋅
2
7
+
⋯
)
∑
n
=
1
∞
1
n
3
=
1
1
3
+
1
2
3
+
1
3
3
+
1
4
3
+
1
5
3
+
⋯
=
Doc 3
0.3777
0.3777
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
ln
2
=
1
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
.
Doc 4
0.3756
1.9475
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1
1
-
1
2
+
1
4
-
1
8
+
1
16
-
1
32
+
⋯
=
2
3
.
1
1
-
1
2
+
1
3
-
1
4
+
1
5
⋯
=
ln
(
2
)
1
1
+
1
2
+
1
4
+
1
8
+
1
16
+
1
32
+
⋯
=
2.
1
1
+
1
3
+
1
6
+
1
10
+
1
15
+
1
21
+
⋯
=
2.
1
1
+
1
1
+
1
2
+
1
6
+
1
24
+
1
120
+
⋯
=
e
.
1
1
+
1
1
+
1
2
+
1
3
+
1
5
+
1
8
+
⋯
=
ψ
.
1
1
+
1
4
+
1
9
+
1
16
+
1
25
+
1
36
+
⋯
=
π
2
6
.
1
1
+
1
2
+
1
3
+
1
4
+
1
5
+
1
6
+
⋯
→
∞
.
Doc 5
0.3649
1.1741
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
1
-
1
2
-
1
4
+
1
3
-
1
6
-
1
8
+
1
5
-
1
10
-
1
12
+
⋯
1
-
1
2
+
1
3
-
1
4
+
⋯
1
2
-
1
4
+
1
6
-
1
8
+
1
10
+
⋯
+
1
2
(
2
k
-
1
)
-
1
2
(
2
k
)
+
⋯
1
2
k
-
1
-
1
2
(
2
k
-
1
)
-
1
4
k
,
k
=
1
,
2
,
…
.
1
+
1
3
+
⋯
+
1
2
a
-
1
-
1
2
-
1
4
-
⋯
-
1
2
b
+
1
2
a
+
1
+
⋯
+
1
4
a
-
1
-
1
2
b
+
2
-
⋯
Doc 6
0.3515
1.3607
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
=
ln
2.
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
∑
n
=
0
∞
(
-
1
)
n
2
n
+
1
=
1
-
1
3
+
1
5
-
1
7
+
⋯
=
π
4
.
area of
rectangles
=
1
+
1
2
+
1
3
+
1
4
+
1
5
+
⋯
.
1
+
1
2
+
1
3
+
1
4
+
1
5
+
1
6
+
1
7
+
1
8
+
1
9
+
⋯
∑
n
=
1
∞
1
n
=
1
+
1
2
+
1
3
+
1
4
+
1
5
+
⋯
.
Doc 7
0.3359
0.5316
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1::2_−_1::4_+_1::8_−_1::16_+_⋯.html
1
-
1
2
-
1
4
+
1
8
-
1
16
+
⋯
=
1
3
.
1
2
-
1
4
+
1
8
-
1
16
+
⋯
=
1
/
2
1
-
(
-
1
/
2
)
=
1
3
.
Doc 8
0.3333
0.3333
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Special_values_of_L-functions.html
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
=
π
4
,
Doc 9
0.3333
0.3333
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Leibniz_formula_for_π.html
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
=
π
4
.
Doc 10
0.3248
0.3248
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
2
3
-
1
2
=
4
6
-
3
6
=
1
6
Doc 11
0.2954
0.6931
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
∑
n
=
0
∞
(
(
-
1
)
n
2
n
+
1
)
1
=
1
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
=
arctan
1
=
π
4
∑
n
=
0
∞
(
(
-
1
)
n
2
n
+
1
)
3
=
1
1
3
-
1
3
3
+
1
5
3
-
1
7
3
+
⋯
=
π
3
32
∑
n
=
0
∞
(
(
-
1
)
n
2
n
+
1
)
5
=
1
1
5
-
1
3
5
+
1
5
5
-
1
7
5
+
⋯
=
5
π
5
1536
Doc 12
0.2939
0.7536
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
π
=
4
1
-
4
3
+
4
5
-
4
7
+
4
9
-
4
11
+
4
13
-
⋯
π
=
4
1
-
4
3
+
4
5
-
4
7
+
4
9
-
4
11
+
4
13
⋯
.
π
2
6
=
1
1
2
+
1
2
2
+
1
3
2
+
1
4
2
+
⋯
Doc 13
0.2874
0.8314
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
1
+
1
2
+
1
4
+
1
8
+
⋯
+
1
2
n
+
⋯
.
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
=
∑
n
=
1
∞
(
-
1
)
n
+
1
1
n
=
ln
(
2
)
.
1
+
1
2
+
1
3
+
1
4
+
1
5
+
⋯
=
∑
n
=
1
∞
1
n
.
Doc 14
0.2725
0.2725
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sylvester's_sequence.html
1
=
1
2
+
1
3
+
1
7
+
1
43
+
1
1807
+
⋯
.
Doc 15
0.2630
0.2630
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Cahen's_constant.html
C
=
∑
(
-
1
)
i
s
i
-
1
=
1
1
-
1
2
+
1
6
-
1
42
+
1
1806
-
⋯
≈
0.64341054629.
Doc 16
0.2623
0.6934
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
π
4
=
3
4
+
1
3
3
-
3
-
1
5
3
-
5
+
1
7
3
-
7
-
⋯
π
4
=
1
-
1
3
+
1
5
-
1
7
+
⋯
cos
x
=
1
-
x
2
2
!
+
x
4
4
!
-
x
6
6
!
+
⋯
Doc 17
0.2623
0.6750
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
π
4
=
3
4
+
1
3
3
-
3
-
1
5
3
-
5
+
1
7
3
-
7
-
⋯
π
4
=
1
-
1
3
+
1
5
-
1
7
+
…
cos
x
=
1
-
x
2
2
!
+
x
4
4
!
-
x
6
6
!
+
⋯
Doc 18
0.2426
0.2426
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Van_Wijngaarden_transformation.html
1
-
1
3
+
1
5
-
1
7
+
⋯
=
π
4
=
0.7853981
…
Doc 19
0.2424
0.6088
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Alternating_series.html
η
(
s
)
=
∑
n
=
1
∞
(
-
1
)
n
-
1
n
s
=
1
1
s
-
1
2
s
+
1
3
s
-
1
4
s
+
⋯
ln
(
2
)
=
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
1
-
1
2
+
1
3
-
1
4
+
⋯
.
(
1
-
1
2
)
-
1
4
+
(
1
3
-
1
6
)
-
1
8
+
(
1
5
-
1
10
)
-
1
12
+
⋯
Doc 20
0.2424
0.2424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_eta_function.html
η
(
s
)
=
∑
n
=
1
∞
(
-
1
)
n
-
1
n
s
=
1
1
s
-
1
2
s
+
1
3
s
-
1
4
s
+
⋯
Doc 21
0.2399
0.2399
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
1
18
=
1
2
-
1
3
-
1
3
2
.
Doc 22
0.2349
0.2349
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/File:GeometricSegment.png.html
1
2
+
1
4
+
1
8
+
1
16
+
⋯
=
1
Doc 23
0.2306
0.2306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Conditional_convergence.html
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
=
∑
n
=
1
∞
(
-
1
)
n
+
1
n
Doc 24
0.2270
0.2270
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Irrationality_sequence.html
1
2
+
1
3
+
1
7
+
1
43
+
⋯
=
1
,
Doc 25
0.2260
0.2260
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Biexciton.html
V
=
2
(
1
r
12
-
1
r
1
a
-
1
r
1
b
-
1
r
2
a
-
1
r
2
b
+
1
r
a
b
)
Doc 26
0.2195
0.2195
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
1
2
+
1
3
+
1
5
+
1
7
+
1
11
+
⋯
→
∞
.
Doc 27
0.2167
0.2167
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
π
=
4
1
+
1
2
3
+
2
2
5
+
3
2
7
+
⋱
=
4
-
1
+
1
6
-
1
34
+
16
3145
-
4
4551
+
1
6601
-
1
38341
+
-
⋯
Doc 28
0.2167
0.3942
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
8
11
=
1
2
+
1
22
+
1
6
+
1
66
.
5
12
=
1
4
+
1
10
+
1
15
=
1
5
+
1
6
+
1
20
.
Doc 29
0.2134
0.8535
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
50
+
1
30
+
1
150
+
1
400
=
1
16
1
50
+
1
30
+
1
150
+
1
400
=
1
16
1
25
+
1
15
+
1
75
+
1
200
=
1
8
1
25
+
1
15
+
1
75
+
1
200
=
1
8
Doc 30
0.2118
0.2118
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Yuktibhāṣā.html
π
4
=
1
-
1
3
+
1
5
-
1
7
+
⋯
+
(
-
1
)
n
2
n
+
1
+
⋯
Doc 31
0.2118
0.2118
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Madhava_of_Sangamagrama.html
π
4
=
1
-
1
3
+
1
5
-
1
7
+
⋯
+
(
-
1
)
n
2
n
+
1
+
⋯
Doc 32
0.2105
0.2105
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Genetic_drift.html
1
2
⋅
1
2
⋅
1
2
⋅
1
2
=
1
16
.
Doc 33
0.2062
0.2062
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kepler's_laws_of_planetary_motion.html
1
r
min
-
1
p
=
1
p
-
1
r
max
Doc 34
0.2048
0.2048
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Greedy_algorithm_for_Egyptian_fractions.html
φ
=
1
1
+
1
2
+
1
9
+
1
145
+
1
37986
+
⋯
Doc 35
0.1994
0.1994
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Logarithmic_growth.html
1
+
1
2
+
1
3
+
1
4
+
1
5
+
⋯
Doc 36
0.1984
0.1984
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Cours_d'Analyse.html
1
4
,
1
3
,
1
6
,
1
5
,
1
8
,
1
7
,
…
Doc 37
0.1957
0.1957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Geometric_progression.html
1
2
-
1
4
+
1
8
-
1
16
+
⋯
=
1
/
2
1
-
(
-
1
/
2
)
=
1
3
.
Doc 38
0.1928
0.3572
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
∏
p
(
1
-
3
p
3
+
2
p
4
+
1
p
5
-
1
p
6
)
=
0.678234...
π
/
4
=
∑
n
=
0
∞
(
-
1
)
n
2
n
+
1
=
1
-
1
3
+
1
5
-
1
7
+
⋯
,
Doc 39
0.1864
0.1864
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Rhind_Mathematical_Papyrus_2::n_table.html
2
n
=
1
n
+
1
2
n
+
1
3
n
+
1
6
n
Doc 40
0.1815
0.1815
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_4_−_8_+_⋯.html
a
0
2
-
Δ
a
0
4
+
Δ
2
a
0
8
-
Δ
3
a
0
16
+
⋯
=
1
2
-
1
4
+
1
8
-
1
16
+
⋯
.
Doc 41
0.1800
0.1800
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Expected_value.html
∑
i
=
1
∞
x
i
p
i
=
c
(
1
-
1
2
+
1
3
-
1
4
+
⋯
)
Doc 42
0.1796
0.1796
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_trial.html
q
=
1
-
p
=
1
-
1
2
=
1
2
Doc 43
0.1777
0.1777
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Random_permutation_statistics.html
n
!
(
1
-
1
1
!
+
1
2
!
-
1
3
!
+
⋯
±
1
n
!
)
=
n
!
∑
k
=
0
n
(
-
1
)
k
k
!
Doc 44
0.1771
0.1771
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_definite_integrals.html
∫
0
∞
x
e
x
+
1
d
x
=
1
1
2
-
1
2
2
+
1
3
2
-
1
4
2
+
…
=
π
2
12
Doc 45
0.1744
0.1744
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Mass_point_geometry.html
O
1
O
2
B
E
=
B
E
-
B
O
2
-
E
O
1
B
E
=
1
-
B
O
2
B
E
-
E
O
1
B
E
=
1
-
1
2
-
3
13
=
7
26
.
Doc 46
0.1631
0.1631
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Summation_of_Grandi's_series.html
1
-
x
+
x
2
2
!
-
x
3
3
!
+
x
4
4
!
-
⋯
=
e
-
x
Doc 47
0.1590
0.1590
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/2_(number).html
∑
k
=
0
∞
1
2
k
=
1
+
1
2
+
1
4
+
1
8
+
1
16
+
⋯
=
2.
Doc 48
0.1585
0.1585
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Net_run_rate.html
254
147.333
+
199
147.333
+
225
147.333
-
253
150
-
110
150
-
103
150
.
Doc 49
0.1580
0.1580
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Smith–Volterra–Cantor_set.html
∑
n
=
0
∞
2
n
2
2
n
+
2
=
1
4
+
1
8
+
1
16
+
⋯
=
1
2
Doc 50
0.1538
0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
1
1
+
1
2
2
+
3
2
2
=
13
15
=
1
-
1
3
+
1
5
.
Doc 51
0.1502
0.2819
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Taylor_series.html
cos
x
=
1
-
x
2
2
!
+
x
4
4
!
-
⋯
-
x
-
1
2
x
2
-
1
3
x
3
-
1
4
x
4
-
⋯
Doc 52
0.1445
0.1445
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Divergence_of_the_sum_of_the_reciprocals_of_the_primes.html
∑
n
=
1
∞
1
n
=
1
+
1
2
+
1
3
+
1
4
+
⋯
Doc 53
0.1422
0.1422
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Divergent_series.html
1
+
1
2
+
1
3
+
1
4
+
1
5
+
⋯
=
∑
n
=
1
∞
1
n
.
Doc 54
0.1378
0.1378
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
π
4
=
1
1
+
1
2
2
+
3
2
2
+
5
2
2
+
⋱
=
1
-
1
3
+
1
5
-
1
7
+
-
…
Doc 55
0.1027
0.1027
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_3_−_4_+_⋯.html
1
2
a
0
-
1
4
Δ
a
0
+
1
8
Δ
2
a
0
-
⋯
=
1
2
-
1
4
.