Đặt f(n) = (n^2 +n+1)^2 +1 xét dãy số (un)
Giải thích
Đáp án D
Ta có
fn=n2+1+n2+1=n2+12+2nn2+1+n2+1
=n2+1n2+1+2n+1=n2+1n2+1+1.
Do đó
f2n−1f2n=2n−12+1.2n2+12n2+1.2n+12+1=2n−12+12n+12+1.
Suy ra
un=f1f2.f3f4.f5f6...f2n−1f2n=12+132+1.32+152+1.52+172+1...2n−12+12n+12+1
⇒un=22n+12=12n2+2n+1
⇒limnun=limn2n2+2n+1=12+1n+1n2=12.