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Stewart Calculus Section 11.1
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Calculus II - 20
1.
11.1 Infinite Sequences A
sequence is something like this: = , , ,··· + = +
2.
( )
( ) = =
3.
(
) ( + ) ( ) ( + ) = =
4.
A sequence
{ } has the limit if for every > there is a corresponding integer such that for every > we have | |< We say { } is convergent, and write = or as
5.
What does it
mean? =
6.
Properties: For convergent sequence
{ } and { } ( + )= + ( )= ( )= = ( )= · = if = ( )= if > , >
7.
Some useful theorems:
If for and = = then = . If | |= then = . If ( )= and ( )= then = . If = and ( ) is continuous at then ( ) = ( ).
8.
Some useful examples:
= if > = if = = if < < is divergent otherwise.
9.
Ex: Find
+
10.
Ex: Find
+ = + +
11.
Ex: Find
+ = + + = +
12.
Ex: Find
+ = + + = + = = . +
13.
Ex: Find
14.
Ex: Find
/ Since = = (l’Hospital’s Rule) we have = .
15.
(
) Ex: Find
16.
(
) Ex: Find ( ) Since = = ( ) we have = .
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