ax2+bx+c=0,D=b2−4ac,x1,2=−b±D2aax^2 + bx + c = 0, \quad D = b^2 - 4ac, \quad x_{1,2} = \frac{-b \pm \sqrt{D}}{2a}ax2+bx+c=0,D=b2−4ac,x1,2=2a−b±D
(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2
a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b)
an⋅am=an+m,anam=an−m,(an)m=an⋅ma^n \cdot a^m = a^{n+m}, \quad \frac{a^n}{a^m} = a^{n-m}, \quad (a^n)^m = a^{n \cdot m}an⋅am=an+m,aman=an−m,(an)m=an⋅m
an=a1+d(n−1),Sn=a1+an2⋅na_n = a_1 + d(n-1), \quad S_n = \frac{a_1 + a_n}{2} \cdot nan=a1+d(n−1),Sn=2a1+an⋅n
