Question

Folosind metoda inductiei matematice, sa se demonstreze:

1³+3³+5³+...+(2n-1)³=n²(2n²-1)

Answer 1

Verificare p(1) :  

$1^{3} = 1^{2} (2*1^{2} -1) <=> 1 = 1(2-1) <=>1=1 ( A)$

Presupunem adevarat pt p(n) si calculam p(n+1):

$1^{3}+3^{3}+....+(2n-1)^3+ (2n+1)^3= (n+1)^2(2*(n+1)^2-1)\\1^{3}+3^{3}+....+ (2n-1)^3+ (2n+1)^3 = (n+1)^2(2*(n+1)^2-1)\\n^2(2n^2-1) + (2n+1)^3 = (n+1)^2(2*(n+1)^2-1)$

Calculul atasat in poza.

Sper ca te-am ajutat!

Daca ai intrebari da-mi mesaj.

Spor! :)