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


Mathematical Induction Principle:
Example 6

Problem.  Find the domain of applicability of the statement  Pn :

2n > n2.

Solution.  Let us verify the validity of the given statement for a few values of  n.

The statement  P1  means that  2 > 1. That is true.

Induction hypothesis: Assume that the proofable equality holds true for some integer  n > 1.

Induction step: We have to prove that the truth of  Pn  implies the validity of  Pn+1, that is,

Really,

Hense, the equality.
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