Referat - Metode de raţionament

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metode, ra355ionament
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Metode de rationament
Metoda directa( modus poneus) - pornind de la o propozitie A si folosind principiul silogismului demonstram ca o alta propozitie este adevarata.
Metoda indirecta – reducerea la absurd ce se bazeaza pe echivalenta (p(q) ( ((q((p)
Metoda inductiei
Metoda inductiei
A. Egalitati
P(n): 1+2+3+...+n=n(n+1)/2 n(1
I. P(1): 1=1 (A)
II. P(n) (A)(P(n+1) (A)
P(n+1):1+2+3...+n+(n+1)=(n+1)(n+2)/2
n(n+1)/2+(n+1)=(n+1)(n+2)/2
(n+1)(n+2)/2=(n+1)(n+2)/2 (A)
I+II( P(n) (A) (n(1
Deci: 1+2+3...+n = (k = n(n+1)/2 , n(1

P(n): 1? +2? +3? +...+n?= n(n+1)(2n+1)/6 n(1
I. P(1): 1=1 (A)
II. P(n) (A) (P(n+1) (A)
P(n+1): 12 +22 +32 +...+n2+(n+1)2=(n+1)(n+2)(2n+3)/6
n(n+1)(2n+1)/6+(n+1)? =( n+1)(n+2)(2n+3)/6
(n+1)(n+2)(2n+3)/6=( n+1)(n+2)(2n+3)/6 (A)
I+II(P(n) (A) (n(1
12 +22 +32 + ... +n2 = (k2 = n(n+1)(2n+1)/6, n(1

13+23+33+...+n3= [n(n+1)/2]2 n(1
I...


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