Question

Exercițiile incercuite !!! Va rog dau 45 de puncte nu am mai multe

Answer 1

3. Fiecare termen este egal cu suma celor doi de dinaintea sa => x = 8+5 =13; y= x+8=13+8=21; 4. a(2010) = 2010^2 -2010×2010 +1 = 0+1 =1; 5. a(2010)= (-2)^2010 - 2^2010 +1 = [(-2)^2]^1005 - 2^2010 +1 = 2^2010 - 2^2010 +1 = 0+1 =1; 6. a(n+1) =[(n+1)^2 + n+1 -3]/(n+1)(n+2)=(n^2+2n+1+n-2)/(n+1)(n+2) = (n^2+3n-1)/(n+1)(n+2); a(n+1) - a (n) =[(n^2 +3n-1) - n ×(n-2)×(n^2 + n -3)]/n (n+1)(n+2) =[n^2 + 3n-1 - (n^2 -2n)×(n^2 + n -3)]/n(n+1)(n+2) =[ n^2 + 3n -1-(n^4 + n^3 - 3n^2 - 2n^3 - 2n^2 +6n)] / n×(n+1)(n+2) = (n^2 +3n-1 -n^4 + n^3 +5n^2 -6n)/n(n+1)(n+2) = (-n^4 + n^3 + 6n^2 - 3n -1) /n (n+1)(n+2) = [-n^3(n+1) +3n(n-1) -1]/n×(n+1)×(n+2); 10. x(n+1) = x (n) + 4n +1; x (1) =1 => x (2) = x (1) + 4×1 +1 = 1 + 4 +1 =6; x(3) = x(2) + 4×2 +1 =6+9=15; x (4) = x(3) + 4×3 +1 =15 +13 =28; x (5) = x (4) + 4×4 +1 = 28 +17 =45; 11. x(n) =[(-1 - n )/2] => x(2010) = [(- 1 - 2010) /2] = [-2011/2] = [-1005,2] = -1005