[tex] a_{n}= a_{n-1}=n^2+n=n(n+1)
a_{n}- a_{n-1}=n(n+1)
...........................
a_{n-1}-a_{n-2}=(n-1)n
a_{2}-a_{1}=2*3=6
[/tex]
Adunăm ultimele n-1 relatii obtinand la membru stang o suma telescopică
[tex] a_{n}-a_{1}=2*3+3*4+..........+n(n-1)
a_{n}= 1*2+2*3+3*4+..........+n(n+1)
a_n=1^2+1+2^2+2*+..........+n^2+n
(1^2+2^2+..........+n^2)+(1+2+3+........+n)
[/tex]
[tex] \frac{n(n+1)(2n+1)}{6}+ \frac{n(n+1)}{2} = \frac{n(n+1)(n+2)}{3} [/tex]
