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Binomial Theoram

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Infinite and Finite Sequences
An
infinite sequence
is a function whose domain is the set of natural numbers {1, 2, 3, 4
,…}.
An
finite sequence
is a function whose domain is the set of natural numbers {1, 2, 3, 4
,…,
n
}, where
n
is some natural number.
2, 4, 8, 16, 32,…
terms
2, 4, 6, 8, …, 98, 100
general term
Terms of a Sequences
Because a sequence is a function, it may be described as
f
(
n
) =
a
n
= 2
n
, where
n
is a natural number.
Example:
Write the first three terms of the sequence whose general term is given by
a
n
=
n
3
+ 1.
a
1
= 1
3
+ 1 = 1 + 1 = 2Replace
n
with 1.
a
2
= 2
3
+ 1 = 8 + 1 = 9Replace
n
with 2.
a
3
= 3
3
+ 1 = 27 + 1 = 28Replace
n
with 3.The first three terms are 2, 9, 28, and 65.

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