1 itpi` oeayg
5 libxz
seqpi`l zeqpkzn ze`ad zexcqd ik (dxcbd t"r ,yxetn ote`a) egiked .1
{an }∞
n=1
Pn
1/k}∞
n=1
√ ∞
= { k=1 1/ k}n=1
{an }∞
n=1 = {
k=1
Pn
(`)
(a)
mi`ad zeleabd z` eayg .2
limn→∞ 1000n
n2 −2
√
√
limn→∞ n( n2 + n + 1 − n2 + n − 1)
(
limn→∞
√
(a)
√
3
n −n+n)
√
√
(b)
n4 +n− n3
n2 +n−1)(
√
√
limn→∞ ( 3 n + 1 − 3 n)
limn→∞
limn→∞
limn→∞ 1 −
1
22
1
n2
1−
+
1
32
limn→∞
2
n2
+
... 1 −
1
n2
n
n2 +n+1
n2 +n
limn→∞
(f)
1·3·5...·(2n−1)
(g)
n!
q
limn→∞
(c)
(n−1)!
(d)
n!
... n−1
(e)
n2
3n + (−1)n + 7n
√
√ √
n
limn→∞ 2 · 4 2... · 2 2
√ √
√
√
√
√
limn→∞ ( 2 − 3 2)( 2 − 5 2)...( 2 − 2n+1 2)
limn→∞
(`)
3n2 +3n+5
(h)
(i)
(k)
(l)
ln(ne5 ) ln n
(n)
ln n
el` recn exiaqde ze`ad zexcqd ly miiwlgd zeleabd lk z` e`vn .3
mlek
n
{an }∞
n=1 = n − 7
{an }∞
n=1 =
n
7n +(−7)n
5n
{an }∞
n=1 =
1
h io∞
n
7
cos πn
2
n=1
o∞
(`)
(a)
n=1
√√
√ ∞
n+2 3 n
√
(b)
√
4
2n+ 3n n=1
ekixtd e` egiked .4
lim sup(−an ) = − lim inf(an )
leabd if`
1
an
an > 0 ,n lkl m`
miiw limn→∞ an
(a)
lim sup(an − bn ) = lim sup(an ) − lim sup(bn )
(b)
lim inf(an bn ) = lim inf(an ) lim inf(bn )
(c)
lim sup(an ) lim sup
=1
(`)
miiwzne
!dglvda
2