heir own conclusions that for n number of persons the number of handshakes will be. This can be easily checked for several n values ​​by using the options in MS Excel, as shown in Figure 6. The n values ​​n = 1, 2, 3 ... are entered in the first row. But the values ​​of expression (n-1). n: 2 are calculated in the second row. Besides, the values ​​in Excel spreadsheet can be calculated very quickly by using the sensitive point and dragging it with cursor as far as you wish. br/>
6. Task 2 value representation in Excel spreadsheet
Method of Mathematical Induction
The method of mathematical induction should not be confused with the inductive reasoning, discussed previously. That is, inductive arguments allow us to formulate hypothesis at the end of experiment or observation but they cannot be taken as mathematically correct proof. Whereas the principle of mathematical induction, if correctly applied, is an example of mathematically correct proof. (France, France, Stokenberga, 2011). Idea of ​​mathematical induction has been with us for ages, certainly since the 16 th century, but was made rigorous only in the 19 th century by Augustus de Morgan who, incidentally, also introduced the term "mathematical induction". By now, induction is ubiquitous in mathematics and is taken for granted by every mathematician. Nevertheless, those who are getting into mathematics are likely to need much practice before induction is in their blood.induction is a powerful proof technique that is generally used to prove statements involving whole numbers.proof by mathematical induction has essentially four parts:
. Carefully describe the statement to be proved and any ranges on certain variables. p align="justify">. The base step: prove one or more base cases
. The inductive step: show how the truth of one statement follows from the truth of some previous statement (s). p align="justify">. State the precise conclusion that follows by mathematical induction. br/>
Variants of Finite Mathematical Induction
mathematics induction multimedia training
There are many forms of mathematical induction - weak, strong, and backward, to name a few. In what follows, n is a variable denoting an integer (usually nonnegative) and S (n) denotes a mathematical statement with one or more occurrences of the variable n. (Gunderson, 2011, p. 35). Method of mathematical induction can be successfully illustrated. The assertion S (n) can be depicted with a line of squares:
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If S (1) is veritable, then we can color the first square:
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But the condition "from every natural...
