Mathematical Induction


 

Mathematical Induction logoSubject: Mathematics    Exam: AP EAMCET Engineering

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Important Concepts in Mathematical Induction

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  • Principles of Mathematical Induction

  • Application of Induction



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Important Points

FIRST PRINCIPLE OF MATHEMATICAL INDUCTION
Step I: Actual verification of the proposition for the starting value 'i'.
Step II: Assuming the proposition to be true for 'k', k >=i and then providing that it is true for the value (k+1) which is the next higher integer.
Step III: Combine the two steps or let P(n) be a statement involving natural number n. To prove statement P(n) is true for all natural number we use following process:
1. Prove that P(1) is true.
2. Assume P(k) is true
3. Using (1) and (2) prove that statement is true for n=k+1, i.e., P(k+1) is true.
This is first principle of Mathematical Induction.
SECOND PRINCIPLE OF MATHEMATICAL INDUCTION
Step I: Actual verification of the proposition for the starting value i and (i+1).
Step II: Assuming the proposition to be true for k-1 and then proving that it is true for the value (k+1):k >=i+1.
Step III: Combine the above two steps these are used to solve problem or in 2nd principle of Mathematical Induction following steps are used:
1. Prove that P(1) is true
2. Assume P(n) is true for all natural number such that 2<=n < k
3. Using (1) and (2) prove that P(k+1) is true.
 
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