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Sagot :
d( k+1) is only true when d(k) is true , d(1) should also be true for d(k+1) statement to be true.
What is Mathematical Induction ?
For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.
It is given that
the statement is true for n = k
According to the principle of Mathematical Induction
Let d(n) be a statement involving Natural Number n such that
- [tex]\rm d(1) \;is\; true[/tex]
- [tex]\rm d(m) \;is\; true[/tex]
- [tex]\rm d(m +1)\; is\; true[/tex]
So , the statement d(n) is true for all the n natural numbers.
According to the second principle of Mathematical Induction
Let d(n) be a statement involving Natural number n such that
- [tex]\rm d(1) \;is\; true[/tex]
- [tex]\rm d(m) \;is\; true[/tex] when [tex]\rm d(n) is true[/tex] for all n where 1 ≤ n ≤m .
- Then the statement [tex]\rm d(n) is true[/tex] for all the values of n ( natural number)
Therefore , d( k+1) is only true when d(k) is true , also d(1) should also be true.
To know more about Mathematical Induction
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