Algebra

• Algebraic Equations
• Complex Numbers
• Product and Factoring
• Set Identities
• Sets of Numbers

Functions

• Exponents Functions
• Hyperbolic Functions
• Logarithm Functions
• Roots Functions
• Trigonometry Functions

Analytic geometry

• 2D dimension Lines
• 2D dimension Triangles
• 3D dimension Lines
• 3D dimension Planes
• Related to Circle
• Conic Sections & Foci

Derivatives and Limits

• Common Derivatives
• Higher order Derivatives
• General Common Limits

Indefinite Integrals

• Common Integrals
• Exponential Integrals
• Logarithmic Integrals
• Rational Integrals
• Trigonometric Integrals

Definite integrals

• Exponential Integrals
• Logarithmic Integrals
• Rational Integrals
• Trigonometric Integrals

Series formulas

• Arithmetic and Geometric Series
• Special Power Series
• Taylor Series
• Go to index page

Notation:

Number of terms in the series: n
First term: a1
Nth term: an
Sum of the first n terms: Sn
Difference between successive terms: d
Common ratio: q
Sum to infinity: S

---

Arithmetic Series Formulas:

\[a_n = a_1 + (n-1)d\] \[ a_i = \frac{a_{i-1} + a_{i+1}}{2}\] \[ S_n = \frac{a_1 + a_n}{2} \cdot n\] \[ S_n = \frac{2 \cdot a_1 + (n-1) \cdot d}{2} \cdot n\]

---

Geometric Series Formulas:

\[a_n = a_1 \cdot q^{n-1}\] \[a_i = \sqrt{a_{i-1} \cdot a_{i+1}}\] \[S_n = \frac{a_nq - a_1}{q-1}\] \[S_n = \frac{a_1 \cdot \left(q^n - 1 \right)}{q-1}\] \[S = \frac{a_1}{1-q}, \quad (\text{for } -1 < q < 1) \]