Returned 97 matches (100 formulae, 55 docs)
    Lookup 16.844 ms, Re-ranking 1784.429 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

0.3697
n = 1 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 +

0.3363
1 - 1 2 - 1 4 + 1 3 - 1 6 - 1 8 + 1 5 - 1 10 - 1 12 +

0.3333
1 1 - 1 2 + 1 4 - 1 8 + 1 16 - 1 32 + = 2 3 .

0.3155
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 ,
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 .

0.3003
1 - 1 2 - 1 4 + 1 8 - 1 16 + = 1 3 .

0.2888
1 - 1 2 + 1 3 - 1 4 + 1 5 - = ln 2.

0.2837
3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± )

0.2809
ln 2 = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - .

0.2776
n = 0 ( ( - 1 ) n 2 n + 1 ) 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - = arctan 1 = π 4

0.2722
π 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 -

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

0.2470
n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + 1 5 -

0.2420
2 3 - 1 2 = 4 6 - 3 6 = 1 6

0.2370
x - 1 - 1 2 = 1 + 1 5 + 1 6 + 1 7 + 1 10 + 1 11 + 1 12 +

0.2331
1 1 - 1 2 + 1 3 - 1 4 + 1 5 = ln ( 2 )

0.2326
k = 1 ( - 1 ) k s k - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 ±

0.2295
n = 1 ( - 1 ) n + 1 n ! = 1 1 ! - 1 2 ! + 1 3 ! - 1 4 ! + 1 5 ! - 1 6 ! +

0.2265
n = 1 ( - 1 ) n - 1 2 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 -

0.2262
1 = 1 2 + 1 3 + 1 7 + 1 43 + 1 1807 + .

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 )

0.2259
n = 0 ( - 1 ) n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! +

0.2226
C = ( - 1 ) i s i - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 - 0.64341054629.

0.2206
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -

0.2177
1 - 1 2 + 1 3 - 1 4 +

0.2141
π 4 = 1 - 1 3 + 1 5 - 1 7 +

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

0.2057
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 -

0.2032
1 2 + 1 4 + 1 8 + 1 16 + = 1

0.2004
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 n

0.1975
1 1 + 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + = 2.

0.1963
1 2 + 1 3 + 1 7 + 1 43 + = 1 ,

0.1959
1 18 = 1 2 - 1 3 - 1 3 2 .

0.1946
n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + = π 4 .

0.1922
1 2 = 1 3 + 1 9 + 1 27 + 1 81 +

0.1903
n = 1 1 n 2 n = n = 1 ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 +

0.1897
1 2 + 1 3 + 1 5 + 1 7 + 1 11 + .

0.1887
1 - 1 3 + 1 5 - 1 7 + = π 4 = 0.7853981

0.1878
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 -

0.1869
x = 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8

0.1828
1 + 1 2 + 1 4 + 1 8 + + 1 2 n + .

0.1827
1 1 + 1 3 + 1 6 + 1 10 + 1 15 + 1 21 + = 2.

0.1813
1 = 1 2 + 1 4 + 1 8 + 1 16 +

0.1797
1 2 - 1 4 + 1 6 - 1 8 + 1 10 + + 1 2 ( 2 k - 1 ) - 1 2 ( 2 k ) +

0.1796
8 11 = 1 2 + 1 22 + 1 6 + 1 66 .

0.1794
π 3 32 = n = 1 - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 +

0.1780
η ( s ) = n = 1 ( - 1 ) n - 1 n s = 1 1 s - 1 2 s + 1 3 s - 1 4 s +

0.1774
x - 1 = 1 + 1 3 + 1 5 + 1 6 + 1 7 + 1 9 + 1 10 + 1 11 +

0.1774
π 4 = 1 - 1 3 + 1 5 - 1 7 +

0.1762
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 .

0.1748
p ( 1 - 3 p 3 + 2 p 4 + 1 p 5 - 1 p 6 ) = 0.678234...

0.1737
n = 0 ( ( - 1 ) n 2 n + 1 ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + = π 3 32

0.1711
π 4 = 1 - 1 3 + 1 5 - 1 7 + + ( - 1 ) n 2 n + 1 +

0.1699
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

0.1699
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 1 n = ln ( 2 ) .

0.1683
1 2 - 1 4 + 1 8 - 1 16 + = 1 / 2 1 - ( - 1 / 2 ) = 1 3 .

0.1683
n = 0 ( ( - 1 ) n 2 n + 1 ) 5 = 1 1 5 - 1 3 5 + 1 5 5 - 1 7 5 + = 5 π 5 1536

0.1672
1 2 1 2 1 2 1 2 = 1 16 .

0.1656
1 50 + 1 30 + 1 150 + 1 400 = 1 16
1 25 + 1 15 + 1 75 + 1 200 = 1 8

0.1653
π 2 6 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 +

0.1649
φ = 1 1 + 1 2 + 1 9 + 1 145 + 1 37986 +

0.1633
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 .

0.1631
1 + 1 2 + 1 3 + 1 4 + 1 5 +

0.1623
1 2 k - 1 - 1 2 ( 2 k - 1 ) - 1 4 k , k = 1 , 2 , .

0.1622
= 1 π ( 1 2 - 1 3 2 3 + 1 5 2 5 - 1 7 2 7 + )

0.1597
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 + -

0.1588
1 1 + 1 4 + 1 9 + 1 16 + 1 25 + 1 36 + = π 2 6 .

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

0.1583
5 12 = 1 4 + 1 10 + 1 15 = 1 5 + 1 6 + 1 20 .

0.1568
n = 1 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + =

0.1566
cos x = 1 - x 2 2 ! + x 4 4 ! - x 6 6 ! +

0.1557
i = 1 x i p i = c ( 1 - 1 2 + 1 3 - 1 4 + )

0.1538
n ! ( 1 - 1 1 ! + 1 2 ! - 1 3 ! + ± 1 n ! ) = n ! k = 0 n ( - 1 ) k k !

0.1534
1 4 , 1 3 , 1 6 , 1 5 , 1 8 , 1 7 ,

0.1524
1 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + .

0.1524
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 + .

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

0.1479
2 n = 1 n + 1 2 n + 1 3 n + 1 6 n

0.1461
ln ( 2 ) = n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + .

0.1448
0 x e x + 1 d x = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + = π 2 12

0.1411
( 1 - 1 2 ) - 1 4 + ( 1 3 - 1 6 ) - 1 8 + ( 1 5 - 1 10 ) - 1 12 +

0.1399
area of rectangles = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .

0.1393
π / 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + ,

0.1382
k = 0 1 2 k = 1 + 1 2 + 1 4 + 1 8 + 1 16 + = 2.

0.1371
1 - x + x 2 2 ! - x 3 3 ! + x 4 4 ! - = e - x

0.1360
1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8 + 1 9 +

0.1358
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 .

0.1301
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 -

0.1298
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .

0.1295
n = 0 2 n 2 2 n + 2 = 1 4 + 1 8 + 1 16 + = 1 2

0.1238
q = 1 - p = 1 - 1 2 = 1 2

0.1190
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 +

0.1183
- x - 1 2 x 2 - 1 3 x 3 - 1 4 x 4 -

0.1164
1 + 1 2 + 1 3 + 1 4 + 1 5 + = n = 1 1 n .

0.1154
1 1 + 1 2 2 + 3 2 2 = 13 15 = 1 - 1 3 + 1 5 .

0.1117
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + = 1 - 1 3 + 1 5 - 1 7 + -

0.0964
1 2 a 0 - 1 4 Δ a 0 + 1 8 Δ 2 a 0 - = 1 2 - 1 4 .