Sequence is a hit of numbers / functions that get got rules or ways of aligning them.
Example:
1, 3, 5, 7, ...
2, 4, 8, 16, ....
Each lay out is called the term of the sequence.
The full general form:
u1, u2, u3, ..., un or (un)
un = tribe-n
n = the lay out of tribes
If the numbers of the sequences are summed upwards at that spot is a shape called a series, which is commonly abbreviated every bit Sn.
Example:
1 + iii + five + vii + ....
2 + iv + 8 + sixteen + ....
The full general form:
The serial is the lay out of rows.
Both the sequence in addition to the serial are functions of n or n variant, n is a tribe number.
Example:
sequence : f(n) = Sn = 3n - 1
Then the sequence is 2, 5, 8, 11, ...
L said limit (un), when for pocket-sized positive numbers ε (eposilon) are defined, tin dismiss endure establish index n1 such that for each n > n1 value apply |L-un| < ∈, written limit n→∞ un = L
The pregnant in addition to the quantity of the Definition tin dismiss sympathize the next example:
The sequence (un), un = 2n/(n + 1), L = 2, ∈ = 1/1000, tin dismiss it actually endure determined n1 such that for n > n1, applicable |2 - (2n/(n+1))| < 1/1000?
limit n→∞ (2n/(n+1)) = 2 → |2 - (2n/(n+1))| < 1/1000 → |(2n + two - 2n)/(n+1)| < 1/1000
|2/(n+1)| < 1/1000 → n + one > 2000 → n > 1999
It turns out to endure establish n1 = 2000
The sequence is called convergent when the tribes get got a limit (n → ∞) which finite, inwards other respects called divergent.
Example:
(un) = 1/2, 3/3, 5/4, 7/5, 9/6, ... , (2n - 1)/(n + 1).
The tribes of the ranks are increase, simply limited.
limit n→∞ un = limit n→∞((2n - 1)/(n + 1)) = 2 → agency (un), konvergen.
Limit properties
So articles at this time.
Sorry if at that spot is a error inwards this article.
Finally I said wassalamualaikum wr. wb.
Reference:
- Calculus Book (WIKARIA GAZALI SOEDADYATMODJO)