INDEX
Numbers and Sets
Complex Numbers
Exponentiation
Algebraic Transformations
Algebraic Equations and Inequalities
Functions
Basic Formulas
Graphics of Basic Functions
Discrete Algebra
Ship 2

Binomial Theorem

Sigma-Notations

Arithmetic Progressions

Geometric Progressions

Binomial Theorem

Pascal's Triangle

Evaluation of Sums of the Form
1k + 2k + ... + nk

1 + 2 + ... + n

1² + 2² + ... + n²

1³ + 2³ + ... + n³

Mathematical Induction Principle

Basic Conceptions

Constituents of the Induction Principle

Model Examples
  Example 1
  Example 2
  Example 3
  Example 4
  Example 5
  Example 6


∑ – Notations
Key Topics Remaining:   Arithmetic Progressions » Geometric Progressions » Binomial Theorem » Pascal's Triangle » Basic Conceptions of the Mathematical Induction Principle » Constituents of the Induction Principle » Model Examples

A sum of indexed numbers is usually written by making use of the ∑–notation:

.

Any letter can be used as the index of summation:

.

The following simple formulas are useful in algebraic transformations of the expression:


Examples
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