Theory of combinations. Newton’s binomial Permutations. Factorial. Arrangements. Combinations. Newton's binomial. Binomial coefficients. Pascal's triangle. Properties of binomial coefficients. By the general name “combinations” we call three kinds of combinations, composed from some number of different elements, belonging to the same set ( for instance, letters … [Read more...]

## Logarithms

Logarithms Logarithm. Main logarithmic identity. P roperties of logarithms. Common logarithm. Natural logarithm. A logarithm of a positive number N to the base b ( b > 0, b1 ) is called an exponent of a power x , to which b must be raised to receive N . The designation: & nbsp; &n bsp; This record is identical … [Read more...]

## Arithmetic and geometric progressions

Arithmetic and geometric progressions Sequences. Numerical sequences. General term of numerical sequence. Arithmetic progression. Geometric progression. Infinitely decreasing geometric progression. Converting of repeating decimal to vulgar fraction.Sequences. Let’s consider the series of natural numbers: 1, 2, 3, … , n – 1, n , … .If to replace each natural number n … [Read more...]

## Proving and solving of inequalities

Proving and solving of inequalities Proving of inequalities. Basic methods. Solving of inequalities. Equivalent inequalities. Method of intervals. Double inequality. Systems of simultaneous inequalities.Proving of inequalities. There are some ways to prove inequalities. We’ll consider them to prove the inequality: where a – a positive number .1). Using of the … [Read more...]

## Inequalities: common information

Inequalities: common information Inequality. Signs of inequalities. Identical inequality. Strict inequality. Non-strict inequality. Solving of inequality or system of simultaneous inequalities. Main properties of inequalities. Some important inequalities. Two expressions ( numerical … [Read more...]