Author: Krystian Karczyński

Granica ciągu z dwiema zmiksowanymi sumami ciągów arytmetycznych

The Limit of a Sequence with Two Mixed Sums of Arithmetic Sequences

Sequence limits sometimes use formulas for the sum of arithmetic or geometric sequences. It's worse if these sequences...

Granica funkcji z podstawieniem

Limit of a Function with Substitution

Harder function limits to calculate often require substitution. Here is an example. Learn detailed methods for calculating function...

Układ równań z parametrem do wyznaczenia

System of Equations with a Parameter to Determine

Calculate "a", knowing that the system of equations is inconsistent. Instead of systematically starting with the rank of...

Granica ciągu z sumą nieskończoną

Limit of a Sequence with an Infinite Sum

Let's take the following sequence limit approaching infinity: (1/{12}+1/{23}+1/{3*4}+...+1/{(n-1)*n}). In the problem, we kind of feel that we...

Rząd macierzy szacowany na oko

Matrix Rank Estimated “By Eye”

Let's assume we have defined the matrix rank as: "the number of linearly independent rows and columns in...