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 ]

1.0000
x - 1 - 1 2 - 1 4 - 1 5 - 1 6 - 1 9 - = 1

0.4034
n = 1 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 +

0.3777
ln 2 = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - .

0.3756
1 1 - 1 2 + 1 4 - 1 8 + 1 16 - 1 32 + = 2 3 .

0.3649
1 - 1 2 - 1 4 + 1 3 - 1 6 - 1 8 + 1 5 - 1 10 - 1 12 +

0.3515
1 - 1 2 + 1 3 - 1 4 + 1 5 - = ln 2.

0.3359
1 - 1 2 - 1 4 + 1 8 - 1 16 + = 1 3 .

0.3333
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 ,
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 .

0.3248
2 3 - 1 2 = 4 6 - 3 6 = 1 6

0.3124
3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± )

0.2954
n = 0 ( ( - 1 ) n 2 n + 1 ) 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - = arctan 1 = π 4

0.2939
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 -

0.2919
π 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 -

0.2900
1 1 - 1 2 + 1 3 - 1 4 + 1 5 = ln ( 2 )

0.2874
n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + 1 5 -

0.2814
k = 1 ( - 1 ) k s k - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 ±

0.2725
1 = 1 2 + 1 3 + 1 7 + 1 43 + 1 1807 + .

0.2704
n = 0 ( - 1 ) n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! +

0.2696
n = 1 ( - 1 ) n + 1 n ! = 1 1 ! - 1 2 ! + 1 3 ! - 1 4 ! + 1 5 ! - 1 6 ! +

0.2687
n = 1 ( - 1 ) n - 1 2 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 -

0.2630
C = ( - 1 ) i s i - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 - 0.64341054629.

0.2623
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -

0.2616
x - 1 = 1 + 1 2 + 1 4 + 1 5 + 1 6 + 1 9 +

0.2569
π 4 = 1 - 1 3 + 1 5 - 1 7 +

0.2531
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 .

0.2517
1 - 1 2 + 1 3 - 1 4 +

0.2500
x - 1 - 1 2 = 1 + 1 5 + 1 6 + 1 7 + 1 10 + 1 11 + 1 12 +

0.2444
1 1 + 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + = 2.

0.2429
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 -

0.2426
1 - 1 3 + 1 5 - 1 7 + = π 4 = 0.7853981

0.2424
η ( s ) = n = 1 ( - 1 ) n - 1 n s = 1 1 s - 1 2 s + 1 3 s - 1 4 s +

0.2399
1 18 = 1 2 - 1 3 - 1 3 2 .

0.2385
π 4 = 1 - 1 3 + 1 5 - 1 7 +

0.2370
1 1 + 1 3 + 1 6 + 1 10 + 1 15 + 1 21 + = 2.

0.2349
1 2 + 1 4 + 1 8 + 1 16 + = 1

0.2342
1 2 = 1 3 + 1 9 + 1 27 + 1 81 +

0.2306
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 n

0.2280
x = 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8

0.2270
1 2 + 1 3 + 1 7 + 1 43 + = 1 ,

0.2267
n = 1 1 n 2 n = n = 1 ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 +

0.2260
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 )

0.2240
n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + = π 4 .

0.2195
1 2 + 1 3 + 1 5 + 1 7 + 1 11 + .

0.2167
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 + -

0.2167
8 11 = 1 2 + 1 22 + 1 6 + 1 66 .

0.2137
π 3 32 = n = 1 - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 +

0.2134
1 50 + 1 30 + 1 150 + 1 400 = 1 16
1 25 + 1 15 + 1 75 + 1 200 = 1 8

0.2119
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 .

0.2118
π 4 = 1 - 1 3 + 1 5 - 1 7 + + ( - 1 ) n 2 n + 1 +

0.2105
1 2 1 2 1 2 1 2 = 1 16 .

0.2085
1 = 1 2 + 1 4 + 1 8 + 1 16 +

0.2080
1 2 - 1 4 + 1 6 - 1 8 + 1 10 + + 1 2 ( 2 k - 1 ) - 1 2 ( 2 k ) +

0.2066
π 2 6 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 +

0.2063
1 + 1 2 + 1 4 + 1 8 + + 1 2 n + .

0.2062
1 r min - 1 p = 1 p - 1 r max

0.2048
φ = 1 1 + 1 2 + 1 9 + 1 145 + 1 37986 +

0.2042
1 2 k - 1 - 1 2 ( 2 k - 1 ) - 1 4 k , k = 1 , 2 , .

0.2020
n = 0 ( ( - 1 ) n 2 n + 1 ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + = π 3 32

0.2018
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

0.2004
ln ( 2 ) = n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + .

0.1994
1 + 1 2 + 1 3 + 1 4 + 1 5 +

0.1984
1 4 , 1 3 , 1 6 , 1 5 , 1 8 , 1 7 ,

0.1957
1 2 - 1 4 + 1 8 - 1 16 + = 1 / 2 1 - ( - 1 / 2 ) = 1 3 .

0.1957
n = 0 ( ( - 1 ) n 2 n + 1 ) 5 = 1 1 5 - 1 3 5 + 1 5 5 - 1 7 5 + = 5 π 5 1536

0.1955
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 1 n = ln ( 2 ) .

0.1952
x - 1 = 1 + 1 3 + 1 5 + 1 6 + 1 7 + 1 9 + 1 10 + 1 11 +

0.1937
= 1 π ( 1 2 - 1 3 2 3 + 1 5 2 5 - 1 7 2 7 + )

0.1928
p ( 1 - 3 p 3 + 2 p 4 + 1 p 5 - 1 p 6 ) = 0.678234...

0.1910
1 1 + 1 4 + 1 9 + 1 16 + 1 25 + 1 36 + = π 2 6 .

0.1886
n = 1 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + =

0.1864
2 n = 1 n + 1 2 n + 1 3 n + 1 6 n

0.1857
1 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + .

0.1815
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 + .

0.1800
i = 1 x i p i = c ( 1 - 1 2 + 1 3 - 1 4 + )

0.1796
q = 1 - p = 1 - 1 2 = 1 2

0.1777
n ! ( 1 - 1 1 ! + 1 2 ! - 1 3 ! + ± 1 n ! ) = n ! k = 0 n ( - 1 ) k k !

0.1775
5 12 = 1 4 + 1 10 + 1 15 = 1 5 + 1 6 + 1 20 .

0.1771
0 x e x + 1 d x = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + = π 2 12

0.1744
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 .

0.1742
cos x = 1 - x 2 2 ! + x 4 4 ! - x 6 6 ! +

0.1710
area of rectangles = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .

0.1682
1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8 + 1 9 +

0.1660
( 1 - 1 2 ) - 1 4 + ( 1 3 - 1 6 ) - 1 8 + ( 1 5 - 1 10 ) - 1 12 +

0.1644
π / 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + ,

0.1631
1 - x + x 2 2 ! - x 3 3 ! + x 4 4 ! - = e - x

0.1590
k = 0 1 2 k = 1 + 1 2 + 1 4 + 1 8 + 1 16 + = 2.

0.1587
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .

0.1585
254 147.333 + 199 147.333 + 225 147.333 - 253 150 - 110 150 - 103 150 .

0.1580
n = 0 2 n 2 2 n + 2 = 1 4 + 1 8 + 1 16 + = 1 2

0.1538
1 1 + 1 2 2 + 3 2 2 = 13 15 = 1 - 1 3 + 1 5 .

0.1502
cos x = 1 - x 2 2 ! + x 4 4 ! -

0.1453
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 -

0.1445
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 +

0.1422
1 + 1 2 + 1 3 + 1 4 + 1 5 + = n = 1 1 n .

0.1378
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + = 1 - 1 3 + 1 5 - 1 7 + -

0.1317
- x - 1 2 x 2 - 1 3 x 3 - 1 4 x 4 -

0.1027
1 2 a 0 - 1 4 Δ a 0 + 1 8 Δ 2 a 0 - = 1 2 - 1 4 .