Discrete Math 2.4 Sequences and Summations
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How long is an empty string?
0
5!
120
0!
1
1!
1
n! basic formula
1 x 2 x ... x n
2!
2
4!
24
9!
362880
10!
3628800
8!
40320
7!
5040
3!
6
6!
720
What is a sequence?
A function from a subset of the set of integers to a set S
What is an arithmetic progressions?
A sequence of the form a, a + d, a + 2d, ... , a + nd, where a and d are real numbers
What is a geometric progression?
A sequence of the form a, ar, ar^2, ... , ar^n where a and r are real numbers
Which linear function is a geometric progression a discrete analogue of?
f(x) = ar^x
Which linear function is an arithmetic progression a discrete analogue of?
f(x) = dx + a
Recursive factorial formula
n! = n x (n - 1)!