Sequences and series Flashcards
-determine the behaviour of some sequences -use sigma notation for series -work with sequences with a constant difference between terms -work with finite series with a constant difference between terms -work with sequences with a constant ratio between terms -work with finite and infinite series with a constant ration between terms -apply sequences to real life problems
what are the 2 ways for which a series can be described
term to term rule
position to term rule (nth term formula)
define an increasing series
where each term is greater than the term before for all n
define a decreasing series
where each term is less than the term before for all n
define a periodic series
a series where terms begine to repeat for some value of k terms.
how do you prove if a series is increasing
if u(n+1)-u(n)>0
how do you prove if a series is decreasing
if u(n+1)-u(n)<0
Process of finding a limit L
as n approaches ∞, u(n+1)=u(n)=L and solve for L for a convergent series
what does ∑ symbol mean
The sum between 2 bounds of a series
∑from 1 to n (r)
1/2 n(n+1)
the nth term of an arithmetic sequence with first term a and common difference d is…
u(n)=a+(n-1)d
∑ n of an arithmetic series with first term a and common difference d
S(n)= n/2 (2a+(n-1)d)
S(n)= n/2 (a+l) where l is the last term
the nth term of an arithmetic sequence with first term a and common ratio r is…
u(n)= ar^n-1
