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


Evaluation of Sums of the Form
1³ + 2³ + … + n³
Key Topics Remaining:   Basic Conceptions of the Mathematical Induction Principle » Constituents of the Induction Principle » Model Examples

Let us consider the sum of the form

.

Perform simple formula manipulations:

Note that

Therefore,

Thus,



Examples
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