Faculty of Management Mathematics Exercises
Sheet 3. Sequences and Their Limits
Exercise 3.1. Give the rst ve terms of each sequence dened below a) an = 2 b) an= n(−1)n c) an= (−1)n
n + 1 + (−1)n 2 d) an = (−1)n+1· 3
n + 1 e) an= −n (2 + (−1)n) Exercise 3.2. Find the limits:
a) lim
n→∞(n2+ 5n − 6) b) lim
n→∞(−2n7+ 3n2− 4) c) lim
n→∞
n2 + 3n n2− 1 d) lim
n→∞
6n3− 1
3n3+ 2n − 4 e) lim
n→∞
n2− 2
n f) lim
n→∞
−3n3+ 1 n2+ 4 g) lim
n→∞
n − 1
n2+ 2n − 1 h) lim
n→∞
n3+ 2n − 1
n4+ n i) lim
n→∞
(1 − 2n)3 (2n + 3)2(1 − 7n) j) lim
n→∞
2n + 3 n + 1
3
k) lim
n→∞
1 − 2n 2 +√
n l) lim
n→∞
2 +√ n 1 − 2n m) lim
n→∞
(3 −√ n)2
5 + 4n n) lim
n→∞
r9n2+ 4n
n2+ 3 o) lim
n→∞
√2n − 1 −√ n − 7 p) lim
n→∞ 3n −√
9n2+ 1
q) lim
n→∞
√4n2+ 9n − 2 − 2n
r) lim
n→∞
√4n2+ 5n − 2 + 2n
s) lim
n→∞ 3n −√
9n2+ 6n − 5
t) lim
n→∞
√n + 1 −√ n
u) lim
n→∞en+1n v) lim
n→∞2n1 w) lim
n→∞
3n− 2n
4n− 3n x) lim
n→∞
4n−1− 5 22n− 7 y) lim
n→∞
2n+1− 3n+2
3n+2 z) lim
n→∞
1 + 1
n
3n
aa) lim
n→∞
1 − 1
3n
n
ab) lim
n→∞
1 + 2 n + 1
n+1
ac) lim
n→∞
n + 4 n
2n
ad) lim
n→∞
n − 1 n + 2
n
ae) lim
n→∞
n2+ 9 n2
n2
af) lim
n→∞
n2− 1 n2
2n2
ag) lim
n→∞
n2 + 2 n2 + 1
n2
ah) lim
n→∞
sin n
n + 1 ai) lim
n→∞
n
n2+ 1sin (3n + 1) aj) lim
n→∞
√3
n2sin n n + 1 ak) lim
n→∞
√n2− 1 −√
n2− 2
al) lim
n→∞
√n4 + n −√
n4− n
am) lim
n→∞
√n2 + 2n − n
an) lim
n→∞
√4n2− 17 − 2n
ao) lim
n→∞
√4n2+ n − 2n
ap) lim
n→∞
√ n2+5−n
√n2+2−n
aq) lim
n→∞
1 + 1
n2
2n2
as) lim
n→∞
n + 1 n
2n+1
at) lim
n→∞
n + 3 n + 2
n
au) lim
n→∞
n2+ 9 n2+ 1
2n2+5
av) lim
n→∞
n + 4 n + 3
5−2n
aw) lim
n→∞
n2+ 2 n2
2n2+1
Last update: November 15, 2010 1