
17-6 Calculus – Differentiation and Integration
Also if lim
n
n
s
→∞
= ∞ then {s
n
} is said to diverge to ¥ and if lim
n
n
s
→∞
= −∞ then {s
n
} is said to
diverge to -¥.
If a sequence neither converge nor it diverges to +¥ or -¥, then the sequence is said to be
oscillating. For instance, the sequence ( ) ,−
∈1
n
n N neither converges nor diverges. It just oscillates.
Example 17.5 Show that the sequence 1,
1
2
,
1
3
,
1
4
,
converges to 0 using the limit definition.
Solution: The above sequence indicates that the terms are getting closer and closer to zero, as they move
along. From the definition of convergence, we need