Đặt f(n) = (n^2 +n+1)^2. xét dãy số (un) sao cho

Đáp án là D.

Ta có

fn=n2+1+n2+1=n2+12+2n.n2+1+n2+1=n2+1n2+1+2n+1

=n2+1n+12+1

Do đó:f2n−1f2n=2n−12+12n2+12n2+12n+12+1=2n−12+12n+12+1

Suy ra

 un=f1.f3.f5...f2n−1f2.f4.f6...f2n=f1f2⋅f3f4⋅f5f6⋅⋅⋅f2n−1f2n

=12+132+1⋅32+152+1⋅52+172+1⋅⋅⋅2n−12+12n+12+1=22n+12+1=12n2+2n+1

⇒nun=n.12n2+2n+1

⇒lim nun=12