n2 + 6n + 9
an = .
2 - n2
3n + 2
lim = 3.
n"
n + 1
{an} {bn}
lim anbn = 0
n"
1 + 2 + · · · + n
cn = sin(2n + n!).
n4
"
"
"
"
3
n3 - 2n + 76 5n2 - 2n4 + 13 3n3 + n 4 3n3 + n2 + 1 + n2
an = , bn = , cn = , dn = .
100n2 + 2n3 + 5 2n + n2 - 1 n4 + 8n - 3n2 2n + 3n2 + 6
p k p, k " N
apnp + ap-1np-1 + ap-2np-2 + · · · + a1n + a0
lim .
n"
bknk + bk-1nk-1 + bk-2nk-2 + · · · + b1n + b0
" - "
lim (3 - 2n3 + 7n2)
n"
" "
lim ( n + 1 - n + 3)
n"
"
lim (n2 - n4 + 6n2)
n"
" "
lim ( n3 + n - n3 + n2 + 1
n"
"
3
lim (n - n3 + 2n + 6)
n"
" "
3 3
lim ( 8n3 + 2n2 - 1 - 8n3 + 2n)
n"
" ["0]
n
lim 2n4 + 5n3 - 2010
n"
"
n
lim 8 · 6n + 7n + 2010 · 2n
n"
n
lim (-1)n + 2n
n"
"
n
lim sin n + 4n + 2009
n"
n -2n
1 3
n
lim 2n + 5 · +
n"
2 5
"
n
lim 5n+10 + 32n-1 + 2009 · 7n+2010
n"
"
n
lim 6n - 5n + 10n2010
n"
"
n
lim 2n3 + 1
n"
"
n
lim 3 · 6n + 2010 · 4n + 2n
n"
n cos n!
lim
n"
2n2 + 3
"
n
lim sin n + 4n + 2009
n"
(-1)n · (n2 + 8)
lim
n"
4n - n3
n n n n
lim + + + · · · +
n"
n2 + 1 n2 + 2 n2 + 3 n2 + n
[1"]
n
n + 1
lim
n"
n + 3
n2+1
1
lim 1 -
n"
n2
n+1
3n2 + 1
lim
n"
n2 + 5
2n2+3
2n3 + n - 1
lim
n"
2n3 + 2n
lim n [ln(n + 1) - ln n]
n"
0
[" · 0]
0
3
lim n sin
n"
n
3
sin
n
lim
5
n"
sin
n
2
lim n
n"
n2
(-21 )
n
lim
7
n"
3n
sin 3n
lim
n"
3n
3n
an =
n!
nn
bn =
(2n)!