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ddrg
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math_formulas

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int64
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24,207
x_{2\cdot n + 1} = \frac{1}{n\cdot 2 + 1}\Longrightarrow 0 = \lim_{n \to \infty} x_{1 + n\cdot 2}
-25,233
\frac{d}{dz} \sqrt{z} = z/2
-16,021
-\frac{1}{10}28 = -5*\frac{8}{10} + 2/10*6
-531
\frac{2}{3}\cdot \pi = -10\cdot \pi + \dfrac{32}{3}\cdot \pi
-12,186
\frac18 \cdot 5 = \frac{1}{8 \cdot \pi} \cdot s \cdot 8 \cdot \pi = s
3,382
\sqrt{3} \cdot 2 + 4 = (\sqrt{3} + 1)^2
5,888
\left(c + f\right) \cdot \left(-c + f\right) = -c \cdot c + f^2
27,917
g*g_l*G = g*g_l*G
-17,787
67 = 13 \left(-1\right) + 80
22,510
\sin(D) = 2\cos(D/2) \sin(D/2)
18,712
29718^2 - 61\times 3805^2 = -1
27,349
d^1 + (-1)^1 = (\left(-1\right) + d)^1
-20,556
\dfrac{1}{54} \cdot (24 - 6 \cdot z) = \frac66 \cdot \frac19 \cdot (4 - z)
1,891
\mathbb{E}(X^4) = 0 \Rightarrow \mathbb{E}(X \times X) = 0
-19,461
\dfrac{7}{2} \div \dfrac{9}{8} = \dfrac{7}{2} \times \dfrac{8}{9}
4,280
\cos{h}*\cos{d} = \tfrac12*\left(\cos\left(h - d\right) + \cos(h + d)\right)
23,125
zz^{-1} = 1 = z^{-1}z
11,523
2 \cdot x + 2 \cdot y' \cdot z + 6 \cdot (-1) + y' \cdot 4 = 0 rightarrow y' = \frac{6 - 2 \cdot x}{2 \cdot z + 4} = \tfrac{1}{z + 2} \cdot (3 - x)
34,206
7/29 \approx 24\% = \tfrac{24}{100}
6,984
\frac{1}{4^n} = \frac{1^n}{4^n} = \left(1/4\right)^n
9,715
12 - 2\cdot x^2 \geq 16 + x^2 - x\cdot 8 \implies 4 + 3\cdot x \cdot x - x\cdot 8 \leq 0
-18,250
\dfrac{1}{z^2 - z*7} \left(7 (-1) + z^2 - z*6\right) = \frac{1}{z*(z + 7 (-1))} (1 + z) (z + 7 (-1))
34,112
6! = \left(4(-1) + 10\right)!
-9,321
-2\cdot 2\cdot 3\cdot 3\cdot n + 2\cdot 3\cdot 7 = -n\cdot 36 + 42
15,438
\tfrac{1}{n!*(n + 2)} = \frac{1}{\left(n + 2\right)!}*(n + 2 + \left(-1\right)) = \frac{1}{(n + 1)!} - \frac{1}{(n + 2)!}
26,377
x^3 + 1 = (x + 1) (-3x + (x + 1)^2)
577
T^4 - 6T^2 + 1 = 8(-1) + (3(-1) + T^2)^2
-10,463
\frac{1}{4 \cdot y} \cdot (2 \cdot y + 10) \cdot 2/2 = \frac{y \cdot 4 + 20}{y \cdot 8}
23,330
\binom{n}{k} = \dfrac{n!}{k!\cdot (-k + n)!}
46,223
Q^\complement = Q^\complement
29,422
D \cup (F \cap X) = (D \cup F) \cap \left(D \cup X\right) = X \cap (D \cup F)
3,841
7 = \frac12\cdot \left(1 + 4 + 9\right)
26,624
(z - 1/2)\times 2 = (-1) + z\times 2
-720
-24\cdot π + \tfrac{299}{12}\cdot π = π\cdot \frac{11}{12}
-9,487
n \cdot 2 \cdot 3 - nn \cdot 2 \cdot 2 \cdot 5 = -n^2 \cdot 20 + n \cdot 6
25,294
-4 - 3*i = (a + x*i) * (a + x*i) = a^2 - x * x + 2*a*x*i
14,416
|z^3 + 3\times z \times z\times h + 3\times z\times h^2 + h^3 - z^3| = |3\times z^2\times h + 3\times z\times h \times h + h^3| \geq 3\times z^2\times h
10,619
\frac{1}{2}(l + k) \leq 0.5 \implies -k - l + 1 = |k + l + (-1)|
3,675
(x\cdot A)^V\cdot F = A^V\cdot x^V\cdot F = A^V\cdot x\cdot F
17,703
n^p + y^p = z^p\Longrightarrow -4*(n*y)^p + (z^2)^p = (n^p - y^p) * (n^p - y^p)
23,871
\frac{1}{|G|}\times |G\times x| = \frac{1}{|G \cap x|}\times |x| = x \cap x/G
46,922
1/13 = \frac{1}{52}4
27,129
(-d + z) \cdot (z^{\left(-1\right) + m} + d \cdot z^{2 \cdot (-1) + m} + \dots + d^{2 \cdot \left(-1\right) + m} \cdot z + d^{m + (-1)}) = z^m - d^m
11,530
m + n + e = m + n + e
-4,055
a^2*9/5 = \frac{9 a^2}{5} 1
35,202
\frac{24541}{7578} = 3 + \dfrac{1}{7578}\cdot 1807
31,646
(a + b + g)*(a * a + b * b + g^2 - a*b - g*b - a*g) = -a*b*g*3 + a^3 + b^3 + g^3
25,793
\frac1D*E = \frac{1}{D}*E
23,843
25 = (-1) \cdot (-25)
24,819
0 = 8(-1) + 2^6 - 2 * 2 * 2*7
40,415
3 = 8 + 5\cdot (-1)
52,111
581 = 490 + 7*13
999
\frac{g}{b} = g/1\times \frac1b = g/(b) = \dfrac{1}{b}\times g
6,560
(a_x + d_x)^2 - a_x^2 - d_x^2 = d_x \cdot 2 \cdot a_x
8,574
\omega\cdot x\cdot 2 + \omega \cdot \omega = -x^2 + \left(x + \omega\right)^2
-2,276
\frac{1}{11}\cdot 4 = 9/11 - 5/11
22,189
(\dfrac{1}{z} + 1 + z)^2 = z \times z + 2 \times z + 3 + \dfrac2z + \dfrac{1}{z \times z}
32,657
x^2 - (x + (-1))^2 = x*2 + \left(-1\right)
18,690
12 + 6 \cdot \left(-1\right) + 1 = 7
-30,277
\frac{1}{(-1) + y} (4 \left(-1\right) + y y + y\cdot 6) = \frac{3}{y + (-1)} + y + 7
-7,047
3/6\times 2/5/4 = \dfrac{1}{20}
22,189
\left(1 + x + \frac{1}{x}\right)^2 = x^2 + 2 \cdot x + 3 + \dfrac{1}{x} \cdot 2 + \frac{1}{x^2}
38,435
\sqrt{124} = \sqrt{2^2\times 31} = \sqrt{2^2}\times \sqrt{31} = 2\times \sqrt{31}
-20,487
(q\cdot 2 + 4)/9\cdot \frac12\cdot 2 = \frac{1}{18}\cdot (8 + q\cdot 4)
-11,553
-16\times i + 2 = -16\times i - 3 + 5
-19,139
7/12 = \frac{1}{36\cdot \pi}\cdot E_t\cdot 36\cdot \pi = E_t
10,175
2\cdot (a^2 + b^2) = \left(a + b\right)^2 + (a - b)^2
17,948
n^{\frac{n}{2}} \cdot n^{\frac{n}{2}} = n^n
27,639
(z^{k_1})^{k_2} = (z^{k_2})^{k_1} = z^{k_1 k_2}
36,828
20 = \left(-32\right)\cdot (-1) - 12
27,440
\frac{1}{135}\times 120 = \dfrac19\times 8
-22,966
90/63 = \frac{9 \cdot 10}{7 \cdot 9}
-19,688
\tfrac{24}{8} = 8\cdot 3/(8)
5,894
\frac{1}{(-1) + 2} \cdot (9 \cdot \left(-1\right) + 12^3 + \left(-1\right)) = 1718
6,952
-\frac{1}{3} = \frac{3 + 4\cdot (-1)}{5 + 2\cdot \left(-1\right)}
24,132
z^3 = 9 + 80^{1 / 2} + 9 - 80^{\frac{1}{2}} + 3((9 + 80^{\frac{1}{2}}) (9 - 80^{\dfrac{1}{2}}))^{1/3} z = 18 + 3z
-18,989
\frac{5}{8} = \dfrac{A_s}{36\cdot \pi}\cdot 36\cdot \pi = A_s
-2,852
(4\cdot 6)^{1/2} + (9\cdot 6)^{1/2} - 6^{1/2} = -6^{1/2} + 24^{1/2} + 54^{1/2}
29,228
\mathbb{P}(n) := \frac{1}{\rho^n} := \left(1/\rho\right)^n
20,883
B = \frac{A}{A - I} = (B - I) A
14,939
\sin(\pi/12) = \dfrac14 \left(-2^{1 / 2} + 6^{1 / 2}\right)
-30,275
x + 4\cdot (-1) - \frac{1}{x + 5\cdot (-1)}\cdot 6 = \dfrac{14 + x^2 - x\cdot 9}{x + 5\cdot (-1)}
19,591
-w \cdot (x + w) \cdot (-x) \cdot 3 = -w \cdot w \cdot w + (w + x)^2 \cdot (w + x) - x^3
50,014
x = (x-1) + 1
5,282
1 + t^2 - t*2 = \left(\left(-1\right) + t\right)^2
-7,986
\dfrac{1}{-i + 2} \times \left(-3 \times i + 6\right) = \dfrac{6 - i \times 3}{2 - i} \times \frac{i + 2}{i + 2}
5,076
(1 - y)^{n + 3 \times (-1)} = (-1)^{n + 3 \times (-1)} \times (y + \left(-1\right))^{n + 3 \times (-1)} = (-1)^{n + (-1)} \times (y + \left(-1\right))^{n + 3 \times (-1)}
28,920
x \cdot x - x \cdot T = T^2 = x \cdot T
-2,836
16^{\dfrac{1}{2}}\cdot 2^{\frac{1}{2}} - 9^{1 / 2}\cdot 2^{\frac{1}{2}} = -2^{1 / 2}\cdot 3 + 2^{\frac{1}{2}}\cdot 4
-20,989
-\dfrac{7}{-63} = \frac19\cdot (\left(-1\right)\cdot 7\cdot 1/(-7))
16,477
m x/b = m/b x = m \frac{x}{b}
2,068
(8 + 6)\cdot (6^{(-1) + n} - 6^{n + 2\cdot (-1)}\cdot 8 + \dotsm - 6\cdot 8^{2\cdot (-1) + n} + 8^{n + (-1)}) = 6^n + 8^n
3,200
0 = 3\cdot (-1) + 3\cdot x^2 \implies x^2 = 1
-1,483
\frac{1/4\cdot (-5)}{(-3)\cdot 1/4} = -\frac13\cdot 4\cdot (-5/4)
33,035
(2 \cdot x) \cdot (2 \cdot x) = 2^2 \cdot x^2 = 4 \cdot x^2
2,650
\sinh(x) + 2.5 = 1\Longrightarrow -1.5 = \sinh(x)
30,041
\frac{1}{2^6}(1^2 + 3^2 + 3^2 + 1^2) = \dfrac{20}{64} = \dfrac{5}{16}
-19,581
3/8\cdot \frac{9}{5} = 3\cdot \frac18/(\frac{1}{9}\cdot 5)
33,312
\dfrac{76!}{76! - 75!} = \frac{75! \cdot 76}{75! \cdot (76 + (-1))} = 76/75
8,033
\dfrac{1}{0.2} + \tfrac{1}{0.5} = 7