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Sequences and Series
Section 12.1 and 12.2
14
Mathematics
Undergraduate 1
10/02/2013

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Cards

Term
Sequence
Definition
set of integers (list of numbers)
Term
Series
Definition
Sum of sequence
Term
Geometric series
Definition
Sum of sequence with a common ratio (r)
Term
How do you know if a sequence is convergent or divergent?
Definition
if the limit to infinity exists sequence is convergent, if DNE then divergent
Term
How do you know if a series is convergent or divergent?
Definition
if the limit to infinity of partial sums exists then the series is convergent, if DNE then divergent
Term
How do you know if a geometric series is convergent or divergent?
Definition
if |r|<1 then convergent, if |r|>_1 then divergent
Term
2^n-1
Definition
2^n*2^-1
Term
lim 1/n!
Definition
0
Term
lim n+1/n
Definition
1
Term
what can you do to: lim ca_n
Definition
c lim a_n
Term
what can you do to: lim a+b
Definition
lim a + lim b
Term
what can you do to: lim a*b
Definition
lim a * lim b
Term
what can you do to: lim a/b
Definition
lim a / lim b (if lim b does not equal 0)
Term
what can you do to: lim (a_n)^p
Definition
(lim a_n)^p
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