A "series" is what you get when you add up all the terms of a sequence; the addition, and also the resulting value, are called the "sum" or the "summation". For instance, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the...
If the probability (loosely speaking) that gk=gk^gk=gk^ is 1/logn1/logn then maybe this can be explained in terms of the multiplicity, in some average sense, of gkgk in a particular finite sequence of gaps. It occurs to me that if the number of gaps less than nn of size (sa...
For Example, calculate the geometric sequence up to 6 terms if first term(a) = 8, and common ratio(r) = 3. The solution for this geometric sequence is explained below: a = 8, d = 3 an= arn - 1 a1(first term) = 8 × 31 - 1= 8 ...
Advanced Topic: Summing an Arithmetic SeriesTo sum up the terms of this arithmetic sequence:a + (a+d) + (a+2d) + (a+3d) + ... use this formula:What is that funny symbol? It is called Sigma Notation Σ (called Sigma) means "sum up" And below and above it are shown the ...
So our infnite geometric series has a finite sum when the ratio is less than 1 (and greater than −1)Let's bring back our previous example, and see what happens:Example: Add up ALL the terms of the Geometric Sequence that halves each time: { 12, 14, 18, 116, ... } We have:...
It is also possible to find a generic term of those sequences using an explicit (that is, exact or definite) formula or explicit equation, for which it suffices to know one term of the sequence and the common difference or common quotient, whose meanings will be explained in the next ...
math,mathematics,maths- a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement patterned advance,progression- a series with a definite pattern of advance Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc...
Among the latter, we find tandem and interspersed repeats [29]. Interspersed repeats are considered transposable elements and will be explained below. Tandem repeats take place when a motif of two or more nucleotides are repeated adjacent to each other in the genome. Depending on the number of ...
(2004) mention that sliding windows, top-down and bottom-up approaches are three principal categories which most time series segmentation algorithms can be grouped into. Keogh et al. (2004) apply those three approaches to the detection of changes in linear trends in 10 different signals and ...
Rather it is the concept that major evolutionary changes, being the consequence of a series of events each of which dependent upon previous ones, can be analyzed properly only within the frame-work of a plausible sequence of events, changes and controlling evolutionary mechanisms. 展开 ...