Question

as vrea sa ma ajutati cu acest exercitiu
la NR1 = a)
NR2 = b)
multumesc frumos

Answer 1

1x4 +2x7+2x10 +...+n(3n+1) = n(n+1)^2 
1) Verificam P(1) :  1x4 = 1(1+1)^2 =1x4   Adevarat !
2) Presupunem ca P(n)este adevarat si calculam P(n+1) 
P (n+1) = (n+1)(n+1+1)^2 =(n+1)(n+2)^2
Dar P(n+1) =1x4+2x7+3x10 +.... +n(3n+1) +(n+1)[3(n+1) +1] 
                  =1x4+2x7+3x10 +.... +n(3n+1) +(n+1)(3n+4) 
P(n+1) =P(n) + (n+1)(3n+4) = n(n+1)^2+ (n+1)(3n+4) =(n+1)(n^2 +n+3n+4)
            =(n+1)(n^2 +4n+4) =(n+1)(n+2)^2
Deci este adevarat !