W6 - Sequence and series Flashcards
(7 cards)
1
Q
Def of Big-O
A
∃c>0 ∃N∈N ∀k>N, f(k)≤c∗g(k)
where f,g: N -> R+ U {0}
2
Q
Arithmetic sequence formula
A
- There is some common difference d such that every term is obtained by adding d to its predecessor
- And a is the first term
Formula is
f_1=a, f_n=f_(n−1)+d
Each term is a, a+d, a+2d
N-th term is a+(n−1)d
3
Q
Finite arithmetic series formula
A
S_n=na+[n(n−1)/2d]
4
Q
Geometric sequences
A
This means there is some common ratio r such that every term is obtained by multiplying its predecessor by r
f_1=a, f_n=f_(n−1)∗r
Each term is a, ar, ar^2
N-th term is a∗r^(n−1)
5
Q
Finite geometric series FORUMLA
A
S_n=a((r^n)−1)/(r−1)
6
Q
Infinite geometric series formula/numbers
A
If r≥1: limit is ∞
If r≤1:
∞ if n is even
-∞ if n is odd
==————-==
if −1<r<1
a/(1-r)
7
Q
Harmonic sequences formula
A
-
(a_n:n∈M)is harmonic if and only if(1/a_n :n∈M)is arithmetic - Sequence where its reciprocals form an arithmetic sequence
