1. lim (√n^2 + n + √n^2+2n + ….. + √n^2+kn – kn), k apartine N*
n->infinit
2. lim (√n^2 + (a-1)n + 6 + 2bn)=2
n->infinit

n n
3. an=Σ (k/n)^2 si an=Σ log(1/3) (k2 + 2k)/(k+1)^2.
k=1 k=1

4. an= (1*1! + 2*2! +…….+n*n!)/(n+1)!
a. Verificati identitatea k*k!=(k+1)! – k!, k apartine N
b. Calculati lim an si lim (an)^(n+1)!
n->infinit n->infinit

Multumesc anticipat!